{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":47078,"title":"Sum of infinite series.","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 169.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 84.9px; transform-origin: 407px 84.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA series T(k,x,n), whose k-th term is given b:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eT(k,x,n) = (x^k)* [ n*(n-1)*....(n-k+1)]/ [k*(k-1).....1] and T(0,x,n) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the sum S = sum(T(k,x,n)) for k = 0 to inf.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ex will greater than -1 and n will be negative.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint: Try binomial expansion or something like binomial compression.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = binomial(x,n)\r\n  S = (1-n)^(x) % something similar can be an easy solution.\r\nend","test_suite":"%%\r\nx = 1;\r\nn = -1;\r\ny_correct = 0.5;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 3;\r\nn = -1;\r\ny_correct = 0.25;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 3;\r\nn = -1;\r\ny_correct = 0.25;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 0;\r\nn = -3;\r\ny_correct = 1;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 3;\r\nn = -1;\r\ny_correct = 0.25;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 1;\r\nn = -2;\r\ny_correct = 0.25;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":442401,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-25T09:23:00.000Z","updated_at":"2026-03-01T15:20:05.000Z","published_at":"2020-10-25T09:23:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA series T(k,x,n), whose k-th term is given b:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(k,x,n) = (x^k)* [ n*(n-1)*....(n-k+1)]/ [k*(k-1).....1] and T(0,x,n) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum S = sum(T(k,x,n)) for k = 0 to inf.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex will greater than -1 and n will be negative.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Try binomial expansion or something like binomial compression.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":785,"title":"Mandelbrot Number Test [Real+Imaginary]","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nMandelbrot numbers remain bounded for n through infinity.\r\nThese numbers have a real and complex component.\r\n\r\nFor a vector of real and complex components determine if each is a Mandelbrot number.\r\n\r\nIf abs(z)\u003e2 then z will escape to infinity and is thus NOT valid.\r\n\r\n*Input:* [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\r\n\r\n*Output:* [1 ; 0 ; 1 ; 0 ; 1 ; 1]\r\n...Where 1 is for a Valid Mandelbrot\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf Chapter 10, Mandelbrot Set (PDF)\u003e\r\n\r\nProblem based upon \u003chttp://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers Cody 81: Mandelbrot Numbers\u003e","description_html":"\u003cp\u003eThe \u003ca href=\"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003eMandelbrot Set\u003c/a\u003e is built around a simple iterative equation.\u003c/p\u003e\u003cpre\u003e z(1)   = c\r\n z(n+1) = z(n)^2 + c\u003c/pre\u003e\u003cp\u003eMandelbrot numbers remain bounded for n through infinity.\r\nThese numbers have a real and complex component.\u003c/p\u003e\u003cp\u003eFor a vector of real and complex components determine if each is a Mandelbrot number.\u003c/p\u003e\u003cp\u003eIf abs(z)\u003e2 then z will escape to infinity and is thus NOT valid.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [1 ; 0 ; 1 ; 0 ; 1 ; 1]\r\n...Where 1 is for a Valid Mandelbrot\u003c/p\u003e\u003cp\u003eCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB: \u003ca href=\"http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf\"\u003eChapter 10, Mandelbrot Set (PDF)\u003c/a\u003e\u003c/p\u003e\u003cp\u003eProblem based upon \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers\"\u003eCody 81: Mandelbrot Numbers\u003c/a\u003e\u003c/p\u003e","function_template":"function tf = isMandelbrot(v)\r\n  tf=abs(v)\u003c=2;\r\nend","test_suite":"%%\r\nformat long\r\n\r\nv=[-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25];\r\ntf=isMandelbrot(v);\r\ntf_expected=[1 ; 0 ; 1 ; 0 ; 1 ; 1] ;\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',tf,tf_expected))\r\n%%\r\n\r\nv=-.25*ones(6,1)+(rand(6,1)-.5)/2+i*(rand(6,1)-.5)/2\r\n\r\n%v=[-.5-.25i;-.5+.25i;-.25i;.25i;-.25-.25i;-.25+.25i]\r\n% Bounding Cases\r\n\r\ntf=isMandelbrot(v);\r\ntf_expected=[1 ; 1 ; 1 ; 1 ; 1 ; 1] ;\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',tf,tf_expected))\r\n%%\r\n\r\nv=rand(6,1)-0.25\r\ntf=isMandelbrot(v);\r\n\r\ntf_expected=v\u003c=0.25; % non-imaginary range [-2.0,0.25]\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',v,tf,tf_expected))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-22T13:35:21.000Z","updated_at":"2026-03-04T14:19:08.000Z","published_at":"2012-07-05T03:42:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot numbers remain bounded for n through infinity. These numbers have a real and complex component.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a vector of real and complex components determine if each is a Mandelbrot number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf abs(z)\u0026gt;2 then z will escape to infinity and is thus NOT valid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [1 ; 0 ; 1 ; 0 ; 1 ; 1] ...Where 1 is for a Valid Mandelbrot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eChapter 10, Mandelbrot Set (PDF)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem based upon\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody 81: Mandelbrot Numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":420,"title":"Sum the Infinite Series II","description":"For any x in the range 0 \u003c x and x \u003c 2*pi radians, find the sum of the following infinite series:\r\n c = 1 + 1/2*cos(x) + 1/2*3/4*cos(2*x) + \r\n     1/2*3/4*5/6*cos(3*x) + 1/2*3/4*5/6*7/8*cos(4*x) + ...\r\nas a function of the form c = infinite_series2(x).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 102.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 51.4333px; transform-origin: 407px 51.4333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 288px 8px; transform-origin: 288px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor any x in the range 0 \u0026lt; x and x \u0026lt; 2*pi radians, find the sum of the following infinite series:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 164px 8.5px; transform-origin: 164px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e c = 1 + 1/2*cos(x) + 1/2*3/4*cos(2*x) + \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 232px 8.5px; transform-origin: 232px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 220px 8.5px; transform-origin: 220px 8.5px; \"\u003e     1/2*3/4*5/6*cos(3*x) + 1/2*3/4*5/6*7/8*cos(4*x) + \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147.5px 8px; transform-origin: 147.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eas a function of the form c = infinite_series2(x).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = infinite_series2(x)\r\n % Compute c here\r\nend","test_suite":"%%\r\nx = 1;\r\nc = infinite_series2(x);\r\nc_correct = 0.8783264829967111;\r\nassert(abs(c-c_correct)\u003c50*eps*abs(c_correct))\r\n\r\n%%   \r\nx = sqrt(3);\r\nc = infinite_series2(x);\r\nc_correct = 0.7603863252347075;\r\nassert(abs(c-c_correct)\u003c50*eps*abs(c_correct))\r\n \r\n% x = 6.28318;\r\n% c = infinite_series2(x);\r\n% c_correct = 306.9401397805991110;\r\n% assert(abs(c-c_correct)\u003c50*eps*abs(c_correct))\r\n\r\n%%\r\nx = 39/7;\r\nc = infinite_series2(x);\r\nc_correct = 0.9836348579190693;\r\nassert(abs(c-c_correct)\u003c50*eps*abs(c_correct))\r\n\r\n%%\r\nx = 1.5e-5;\r\nc = infinite_series2(x);\r\nc_correct = 182.5748704878243416;\r\nassert(abs(c-c_correct)\u003c50*eps*abs(c_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":9,"created_by":28,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2021-07-23T05:57:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-27T05:17:45.000Z","updated_at":"2026-01-20T14:37:34.000Z","published_at":"2012-02-27T16:09:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any x in the range 0 \u0026lt; x and x \u0026lt; 2*pi radians, find the sum of the following infinite series:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = 1 + 1/2*cos(x) + 1/2*3/4*cos(2*x) + \\n     1/2*3/4*5/6*cos(3*x) + 1/2*3/4*5/6*7/8*cos(4*x) + ...]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eas a function of the form c = infinite_series2(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2909,"title":"Approximation of Pi (vector inputs)","description":"Pi (divided by 4) can be approximated by the following infinite series:\r\n\r\npi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\r\n\r\nFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\r\n\r\nThis problem is the same as \u003chttps://www.mathworks.com/matlabcentral/cody/problems/2908-approximation-of-pi Problem 2908\u003e, except that the test suite will pass vectors for the number of terms, rather than breaking each truncated infinite series into a separate test.","description_html":"\u003cp\u003ePi (divided by 4) can be approximated by the following infinite series:\u003c/p\u003e\u003cp\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\u003c/p\u003e\u003cp\u003eFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\u003c/p\u003e\u003cp\u003eThis problem is the same as \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/2908-approximation-of-pi\"\u003eProblem 2908\u003c/a\u003e, except that the test suite will pass vectors for the number of terms, rather than breaking each truncated infinite series into a separate test.\u003c/p\u003e","function_template":"function y = pi_approx(n)\r\n y = n;\r\nend","test_suite":"%%\r\nn = 1:5;\r\ny_correct = [-0.858407346410207 0.474925986923126 -0.325074013076874 0.246354558351698 -0.198089886092747];\r\nanswers = pi_approx(n);\r\nfor i = 1:numel(n)\r\n assert(abs(answers(i)-y_correct(i))\u003c(100*eps))\r\nend\r\n\r\n%%\r\nn = 2:2:10;\r\ny_correct = [0.474925986923126 0.246354558351698 0.165546477543617 0.124520836517975 0.099753034660390];\r\nanswers = pi_approx(n);\r\nfor i = 1:numel(n)\r\n assert(abs(answers(i)-y_correct(i))\u003c(100*eps))\r\nend\r\n\r\n%%\r\nn = 5:5:25;\r\ny_correct = [-0.198089886092747 0.099753034660390 -0.066592998672151 0.049968846921953 -0.039984031845239];\r\nanswers = pi_approx(n);\r\nfor i = 1:numel(n)\r\n assert(abs(answers(i)-y_correct(i))\u003c(100*eps))\r\nend\r\n\r\n%%\r\nn = 10:10:100;\r\ny_correct = [0.099753034660390 0.049968846921953 0.033324086890846 0.024996096795960 0.019998000998782 0.016665509660796 0.014284985608559 0.012499511814072 0.011110768228485 0.009999750031239];\r\nanswers = pi_approx(n);\r\nfor i = 1:numel(n)\r\n assert(abs(answers(i)-y_correct(i))\u003c(100*eps))\r\nend\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":276,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:45:00.000Z","updated_at":"2026-04-01T09:59:49.000Z","published_at":"2015-02-01T03:45:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePi (divided by 4) can be approximated by the following infinite series:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is the same as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2908-approximation-of-pi\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2908\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, except that the test suite will pass vectors for the number of terms, rather than breaking each truncated infinite series into a separate test.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2908,"title":"Approximation of Pi","description":"Pi (divided by 4) can be approximated by the following infinite series:\r\npi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\r\nFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\r\nAlso, try Problem 2909, a slightly harder variant of this problem.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 215px 8px; transform-origin: 215px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePi (divided by 4) can be approximated by the following infinite series:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360px 8px; transform-origin: 360px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.5px 8px; transform-origin: 25.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAlso, try\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2909-approximation-of-pi-vector-inputs\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 2909\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128.5px 8px; transform-origin: 128.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, a slightly harder variant of this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pi_approx(n)\r\n y = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = -0.858407346410207;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 2;\r\ny_correct = 0.474925986923126;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps)) \r\n\r\n%%\r\nn = 4;\r\ny_correct = 0.246354558351698;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 7;\r\ny_correct = -0.142145830148691;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 10;\r\ny_correct = 0.099753034660390;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 14;\r\ny_correct = 0.071338035810608;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 17;\r\ny_correct = -0.058772861819756;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 20;\r\ny_correct = 0.049968846921953;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 25;\r\ny_correct = -0.039984031845239;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 42;\r\ny_correct = 0.023806151830915;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n","published":true,"deleted":false,"likes_count":18,"comments_count":0,"created_by":26769,"edited_by":223089,"edited_at":"2022-09-05T17:21:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1412,"test_suite_updated_at":"2022-09-05T17:21:56.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:29:10.000Z","updated_at":"2026-04-17T02:25:03.000Z","published_at":"2015-02-01T03:29:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePi (divided by 4) can be approximated by the following infinite series:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlso, try\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2909-approximation-of-pi-vector-inputs\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2909\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, a slightly harder variant of this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":415,"title":"Sum the Infinite Series","description":"  Given that 0 \u003c x and x \u003c 2*pi where x is in radians, write a function\r\n\r\n [c,s] = infinite_series(x);\r\n\r\nthat returns with the sums of the two infinite series\r\n\r\n c = cos(2*x)/1/2 + cos(3*x)/2/3 + cos(4*x)/3/4 + ... + cos((n+1)*x)/n/(n+1) + ...\r\n s = sin(2*x)/1/2 + sin(3*x)/2/3 + sin(4*x)/3/4 + ... + sin((n+1)*x)/n/(n+1) + ...\r\n","description_html":"\u003cpre class=\"language-matlab\"\u003eGiven that 0 \u0026lt; x and x \u0026lt; 2*pi where x is in radians, write a function\r\n\u003c/pre\u003e\u003cpre\u003e [c,s] = infinite_series(x);\u003c/pre\u003e\u003cp\u003ethat returns with the sums of the two infinite series\u003c/p\u003e\u003cpre\u003e c = cos(2*x)/1/2 + cos(3*x)/2/3 + cos(4*x)/3/4 + ... + cos((n+1)*x)/n/(n+1) + ...\r\n s = sin(2*x)/1/2 + sin(3*x)/2/3 + sin(4*x)/3/4 + ... + sin((n+1)*x)/n/(n+1) + ...\u003c/pre\u003e","function_template":"function  [c,s] = infinite_series(x)\r\n  c = 0; s = 0;\r\nend","test_suite":"%%\r\nx = 1;      \r\n[c,s] = infinite_series(x);\r\nc_correct = -0.3800580037051224; s_correct =  0.3845865774434312;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = exp(1); \r\n[c,s] = infinite_series(x);\r\nc_correct =  0.2832904461013926; s_correct = -0.2693088098978689;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = sqrt(3);\r\n[c,s] = infinite_series(x);\r\nc_correct = -0.3675627321761342; s_correct = -0.2464611942058812;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = 0.001;  \r\n[c,s] = infinite_series(x);\r\nc_correct =  0.9984257500575904; s_correct =  0.0079069688545917;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = pi/4;   \r\n[c,s] = infinite_series(x);\r\nc_correct = -0.2042534159513846; s_correct =  0.5511304391316155;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = 0.0263; \r\n[c,s] = infinite_series(x);\r\nc_correct =  0.9574346130196565; s_correct =  0.1214323234202421;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = 6.273;  \r\n[c,s] = infinite_series(x);\r\nc_correct =  0.9837633160098646; s_correct = -0.0568212139709541;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = 31/7;   \r\n[c,s] = infinite_series(x);\r\nc_correct = -0.2961416175321223; s_correct =  0.3148962998550185;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":8,"created_by":28,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":143,"test_suite_updated_at":"2012-02-26T05:22:31.000Z","rescore_all_solutions":false,"group_id":27,"created_at":"2012-02-26T05:22:31.000Z","updated_at":"2026-04-16T01:57:27.000Z","published_at":"2012-02-26T05:22:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Given that 0 \u003c x and x \u003c 2*pi where x is in radians, write a function\\n\\n [c,s] = infinite_series(x);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethat returns with the sums of the two infinite series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = cos(2*x)/1/2 + cos(3*x)/2/3 + cos(4*x)/3/4 + ... + cos((n+1)*x)/n/(n+1) + ...\\n s = sin(2*x)/1/2 + sin(3*x)/2/3 + sin(4*x)/3/4 + ... + sin((n+1)*x)/n/(n+1) + ...]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":47078,"title":"Sum of infinite series.","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 169.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 84.9px; transform-origin: 407px 84.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA series T(k,x,n), whose k-th term is given b:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eT(k,x,n) = (x^k)* [ n*(n-1)*....(n-k+1)]/ [k*(k-1).....1] and T(0,x,n) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the sum S = sum(T(k,x,n)) for k = 0 to inf.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ex will greater than -1 and n will be negative.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint: Try binomial expansion or something like binomial compression.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = binomial(x,n)\r\n  S = (1-n)^(x) % something similar can be an easy solution.\r\nend","test_suite":"%%\r\nx = 1;\r\nn = -1;\r\ny_correct = 0.5;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 3;\r\nn = -1;\r\ny_correct = 0.25;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 3;\r\nn = -1;\r\ny_correct = 0.25;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 0;\r\nn = -3;\r\ny_correct = 1;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 3;\r\nn = -1;\r\ny_correct = 0.25;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)\r\n\r\n%%\r\nx = 1;\r\nn = -2;\r\ny_correct = 0.25;\r\nassert(abs(binomial(x,n)-y_correct)\u003c1e-5)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":442401,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-25T09:23:00.000Z","updated_at":"2026-03-01T15:20:05.000Z","published_at":"2020-10-25T09:23:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA series T(k,x,n), whose k-th term is given b:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(k,x,n) = (x^k)* [ n*(n-1)*....(n-k+1)]/ [k*(k-1).....1] and T(0,x,n) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum S = sum(T(k,x,n)) for k = 0 to inf.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex will greater than -1 and n will be negative.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Try binomial expansion or something like binomial compression.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":785,"title":"Mandelbrot Number Test [Real+Imaginary]","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nMandelbrot numbers remain bounded for n through infinity.\r\nThese numbers have a real and complex component.\r\n\r\nFor a vector of real and complex components determine if each is a Mandelbrot number.\r\n\r\nIf abs(z)\u003e2 then z will escape to infinity and is thus NOT valid.\r\n\r\n*Input:* [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\r\n\r\n*Output:* [1 ; 0 ; 1 ; 0 ; 1 ; 1]\r\n...Where 1 is for a Valid Mandelbrot\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf Chapter 10, Mandelbrot Set (PDF)\u003e\r\n\r\nProblem based upon \u003chttp://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers Cody 81: Mandelbrot Numbers\u003e","description_html":"\u003cp\u003eThe \u003ca href=\"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003eMandelbrot Set\u003c/a\u003e is built around a simple iterative equation.\u003c/p\u003e\u003cpre\u003e z(1)   = c\r\n z(n+1) = z(n)^2 + c\u003c/pre\u003e\u003cp\u003eMandelbrot numbers remain bounded for n through infinity.\r\nThese numbers have a real and complex component.\u003c/p\u003e\u003cp\u003eFor a vector of real and complex components determine if each is a Mandelbrot number.\u003c/p\u003e\u003cp\u003eIf abs(z)\u003e2 then z will escape to infinity and is thus NOT valid.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [1 ; 0 ; 1 ; 0 ; 1 ; 1]\r\n...Where 1 is for a Valid Mandelbrot\u003c/p\u003e\u003cp\u003eCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB: \u003ca href=\"http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf\"\u003eChapter 10, Mandelbrot Set (PDF)\u003c/a\u003e\u003c/p\u003e\u003cp\u003eProblem based upon \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers\"\u003eCody 81: Mandelbrot Numbers\u003c/a\u003e\u003c/p\u003e","function_template":"function tf = isMandelbrot(v)\r\n  tf=abs(v)\u003c=2;\r\nend","test_suite":"%%\r\nformat long\r\n\r\nv=[-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25];\r\ntf=isMandelbrot(v);\r\ntf_expected=[1 ; 0 ; 1 ; 0 ; 1 ; 1] ;\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',tf,tf_expected))\r\n%%\r\n\r\nv=-.25*ones(6,1)+(rand(6,1)-.5)/2+i*(rand(6,1)-.5)/2\r\n\r\n%v=[-.5-.25i;-.5+.25i;-.25i;.25i;-.25-.25i;-.25+.25i]\r\n% Bounding Cases\r\n\r\ntf=isMandelbrot(v);\r\ntf_expected=[1 ; 1 ; 1 ; 1 ; 1 ; 1] ;\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',tf,tf_expected))\r\n%%\r\n\r\nv=rand(6,1)-0.25\r\ntf=isMandelbrot(v);\r\n\r\ntf_expected=v\u003c=0.25; % non-imaginary range [-2.0,0.25]\r\n\r\nassert(isequal(tf,tf_expected),sprintf('\\n%f %f %f %f %f %f',v,tf,tf_expected))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-22T13:35:21.000Z","updated_at":"2026-03-04T14:19:08.000Z","published_at":"2012-07-05T03:42:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot numbers remain bounded for n through infinity. These numbers have a real and complex component.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a vector of real and complex components determine if each is a Mandelbrot number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf abs(z)\u0026gt;2 then z will escape to infinity and is thus NOT valid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [1 ; 0 ; 1 ; 0 ; 1 ; 1] ...Where 1 is for a Valid Mandelbrot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eChapter 10, Mandelbrot Set (PDF)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem based upon\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/81-mandelbrot-numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody 81: Mandelbrot Numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":420,"title":"Sum the Infinite Series II","description":"For any x in the range 0 \u003c x and x \u003c 2*pi radians, find the sum of the following infinite series:\r\n c = 1 + 1/2*cos(x) + 1/2*3/4*cos(2*x) + \r\n     1/2*3/4*5/6*cos(3*x) + 1/2*3/4*5/6*7/8*cos(4*x) + ...\r\nas a function of the form c = infinite_series2(x).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 102.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 51.4333px; transform-origin: 407px 51.4333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 288px 8px; transform-origin: 288px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor any x in the range 0 \u0026lt; x and x \u0026lt; 2*pi radians, find the sum of the following infinite series:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 164px 8.5px; transform-origin: 164px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e c = 1 + 1/2*cos(x) + 1/2*3/4*cos(2*x) + \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 232px 8.5px; transform-origin: 232px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 220px 8.5px; transform-origin: 220px 8.5px; \"\u003e     1/2*3/4*5/6*cos(3*x) + 1/2*3/4*5/6*7/8*cos(4*x) + \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration: none; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147.5px 8px; transform-origin: 147.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eas a function of the form c = infinite_series2(x).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = infinite_series2(x)\r\n % Compute c here\r\nend","test_suite":"%%\r\nx = 1;\r\nc = infinite_series2(x);\r\nc_correct = 0.8783264829967111;\r\nassert(abs(c-c_correct)\u003c50*eps*abs(c_correct))\r\n\r\n%%   \r\nx = sqrt(3);\r\nc = infinite_series2(x);\r\nc_correct = 0.7603863252347075;\r\nassert(abs(c-c_correct)\u003c50*eps*abs(c_correct))\r\n \r\n% x = 6.28318;\r\n% c = infinite_series2(x);\r\n% c_correct = 306.9401397805991110;\r\n% assert(abs(c-c_correct)\u003c50*eps*abs(c_correct))\r\n\r\n%%\r\nx = 39/7;\r\nc = infinite_series2(x);\r\nc_correct = 0.9836348579190693;\r\nassert(abs(c-c_correct)\u003c50*eps*abs(c_correct))\r\n\r\n%%\r\nx = 1.5e-5;\r\nc = infinite_series2(x);\r\nc_correct = 182.5748704878243416;\r\nassert(abs(c-c_correct)\u003c50*eps*abs(c_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":9,"created_by":28,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2021-07-23T05:57:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-27T05:17:45.000Z","updated_at":"2026-01-20T14:37:34.000Z","published_at":"2012-02-27T16:09:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any x in the range 0 \u0026lt; x and x \u0026lt; 2*pi radians, find the sum of the following infinite series:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = 1 + 1/2*cos(x) + 1/2*3/4*cos(2*x) + \\n     1/2*3/4*5/6*cos(3*x) + 1/2*3/4*5/6*7/8*cos(4*x) + ...]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eas a function of the form c = infinite_series2(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2909,"title":"Approximation of Pi (vector inputs)","description":"Pi (divided by 4) can be approximated by the following infinite series:\r\n\r\npi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\r\n\r\nFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\r\n\r\nThis problem is the same as \u003chttps://www.mathworks.com/matlabcentral/cody/problems/2908-approximation-of-pi Problem 2908\u003e, except that the test suite will pass vectors for the number of terms, rather than breaking each truncated infinite series into a separate test.","description_html":"\u003cp\u003ePi (divided by 4) can be approximated by the following infinite series:\u003c/p\u003e\u003cp\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\u003c/p\u003e\u003cp\u003eFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\u003c/p\u003e\u003cp\u003eThis problem is the same as \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/2908-approximation-of-pi\"\u003eProblem 2908\u003c/a\u003e, except that the test suite will pass vectors for the number of terms, rather than breaking each truncated infinite series into a separate test.\u003c/p\u003e","function_template":"function y = pi_approx(n)\r\n y = n;\r\nend","test_suite":"%%\r\nn = 1:5;\r\ny_correct = [-0.858407346410207 0.474925986923126 -0.325074013076874 0.246354558351698 -0.198089886092747];\r\nanswers = pi_approx(n);\r\nfor i = 1:numel(n)\r\n assert(abs(answers(i)-y_correct(i))\u003c(100*eps))\r\nend\r\n\r\n%%\r\nn = 2:2:10;\r\ny_correct = [0.474925986923126 0.246354558351698 0.165546477543617 0.124520836517975 0.099753034660390];\r\nanswers = pi_approx(n);\r\nfor i = 1:numel(n)\r\n assert(abs(answers(i)-y_correct(i))\u003c(100*eps))\r\nend\r\n\r\n%%\r\nn = 5:5:25;\r\ny_correct = [-0.198089886092747 0.099753034660390 -0.066592998672151 0.049968846921953 -0.039984031845239];\r\nanswers = pi_approx(n);\r\nfor i = 1:numel(n)\r\n assert(abs(answers(i)-y_correct(i))\u003c(100*eps))\r\nend\r\n\r\n%%\r\nn = 10:10:100;\r\ny_correct = [0.099753034660390 0.049968846921953 0.033324086890846 0.024996096795960 0.019998000998782 0.016665509660796 0.014284985608559 0.012499511814072 0.011110768228485 0.009999750031239];\r\nanswers = pi_approx(n);\r\nfor i = 1:numel(n)\r\n assert(abs(answers(i)-y_correct(i))\u003c(100*eps))\r\nend\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":276,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:45:00.000Z","updated_at":"2026-04-01T09:59:49.000Z","published_at":"2015-02-01T03:45:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePi (divided by 4) can be approximated by the following infinite series:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is the same as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2908-approximation-of-pi\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2908\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, except that the test suite will pass vectors for the number of terms, rather than breaking each truncated infinite series into a separate test.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2908,"title":"Approximation of Pi","description":"Pi (divided by 4) can be approximated by the following infinite series:\r\npi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\r\nFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\r\nAlso, try Problem 2909, a slightly harder variant of this problem.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 215px 8px; transform-origin: 215px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePi (divided by 4) can be approximated by the following infinite series:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360px 8px; transform-origin: 360px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.5px 8px; transform-origin: 25.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAlso, try\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2909-approximation-of-pi-vector-inputs\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 2909\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128.5px 8px; transform-origin: 128.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, a slightly harder variant of this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pi_approx(n)\r\n y = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = -0.858407346410207;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 2;\r\ny_correct = 0.474925986923126;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps)) \r\n\r\n%%\r\nn = 4;\r\ny_correct = 0.246354558351698;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 7;\r\ny_correct = -0.142145830148691;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 10;\r\ny_correct = 0.099753034660390;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 14;\r\ny_correct = 0.071338035810608;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 17;\r\ny_correct = -0.058772861819756;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 20;\r\ny_correct = 0.049968846921953;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 25;\r\ny_correct = -0.039984031845239;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 42;\r\ny_correct = 0.023806151830915;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n","published":true,"deleted":false,"likes_count":18,"comments_count":0,"created_by":26769,"edited_by":223089,"edited_at":"2022-09-05T17:21:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1412,"test_suite_updated_at":"2022-09-05T17:21:56.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:29:10.000Z","updated_at":"2026-04-17T02:25:03.000Z","published_at":"2015-02-01T03:29:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePi (divided by 4) can be approximated by the following infinite series:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlso, try\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2909-approximation-of-pi-vector-inputs\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2909\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, a slightly harder variant of this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":415,"title":"Sum the Infinite Series","description":"  Given that 0 \u003c x and x \u003c 2*pi where x is in radians, write a function\r\n\r\n [c,s] = infinite_series(x);\r\n\r\nthat returns with the sums of the two infinite series\r\n\r\n c = cos(2*x)/1/2 + cos(3*x)/2/3 + cos(4*x)/3/4 + ... + cos((n+1)*x)/n/(n+1) + ...\r\n s = sin(2*x)/1/2 + sin(3*x)/2/3 + sin(4*x)/3/4 + ... + sin((n+1)*x)/n/(n+1) + ...\r\n","description_html":"\u003cpre class=\"language-matlab\"\u003eGiven that 0 \u0026lt; x and x \u0026lt; 2*pi where x is in radians, write a function\r\n\u003c/pre\u003e\u003cpre\u003e [c,s] = infinite_series(x);\u003c/pre\u003e\u003cp\u003ethat returns with the sums of the two infinite series\u003c/p\u003e\u003cpre\u003e c = cos(2*x)/1/2 + cos(3*x)/2/3 + cos(4*x)/3/4 + ... + cos((n+1)*x)/n/(n+1) + ...\r\n s = sin(2*x)/1/2 + sin(3*x)/2/3 + sin(4*x)/3/4 + ... + sin((n+1)*x)/n/(n+1) + ...\u003c/pre\u003e","function_template":"function  [c,s] = infinite_series(x)\r\n  c = 0; s = 0;\r\nend","test_suite":"%%\r\nx = 1;      \r\n[c,s] = infinite_series(x);\r\nc_correct = -0.3800580037051224; s_correct =  0.3845865774434312;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = exp(1); \r\n[c,s] = infinite_series(x);\r\nc_correct =  0.2832904461013926; s_correct = -0.2693088098978689;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = sqrt(3);\r\n[c,s] = infinite_series(x);\r\nc_correct = -0.3675627321761342; s_correct = -0.2464611942058812;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = 0.001;  \r\n[c,s] = infinite_series(x);\r\nc_correct =  0.9984257500575904; s_correct =  0.0079069688545917;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = pi/4;   \r\n[c,s] = infinite_series(x);\r\nc_correct = -0.2042534159513846; s_correct =  0.5511304391316155;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = 0.0263; \r\n[c,s] = infinite_series(x);\r\nc_correct =  0.9574346130196565; s_correct =  0.1214323234202421;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = 6.273;  \r\n[c,s] = infinite_series(x);\r\nc_correct =  0.9837633160098646; s_correct = -0.0568212139709541;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n%%\r\nx = 31/7;   \r\n[c,s] = infinite_series(x);\r\nc_correct = -0.2961416175321223; s_correct =  0.3148962998550185;\r\nassert(abs(c-c_correct)\u003c50*eps \u0026 abs(s-s_correct)\u003c50*eps)\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":8,"created_by":28,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":143,"test_suite_updated_at":"2012-02-26T05:22:31.000Z","rescore_all_solutions":false,"group_id":27,"created_at":"2012-02-26T05:22:31.000Z","updated_at":"2026-04-16T01:57:27.000Z","published_at":"2012-02-26T05:22:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Given that 0 \u003c x and x \u003c 2*pi where x is in radians, write a function\\n\\n [c,s] = infinite_series(x);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethat returns with the sums of the two infinite series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = cos(2*x)/1/2 + cos(3*x)/2/3 + cos(4*x)/3/4 + ... + cos((n+1)*x)/n/(n+1) + ...\\n s = sin(2*x)/1/2 + sin(3*x)/2/3 + sin(4*x)/3/4 + ... + sin((n+1)*x)/n/(n+1) + 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