{"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":58274,"title":"Easy Sequences 116: Summation involving nthroot, floor, and ceiling functions","description":"Given a postive integers  and , we are asked to evaluate the following summation:\r\n                            \r\n                            where: the symbol \"\" and \"\" are the floor and ceil functions, respectively.\r\nFor example, if  and , we have:\r\n\u003e\u003e  S = @(x,n) sum(arrayfun(@(i) ceil(nthroot(i-1,n))+floor(nthroot(i+1,n)),1:x));\r\n\u003e\u003e  s = S(50,3)\r\n\u003e\u003e  s =\r\n        279","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; 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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 226px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 113px; transform-origin: 407px 113px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a postive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; 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 23px; text-align: left; transform-origin: 384px 23px; 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\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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GUycaeTPUaFZCq8TPiSsJmwlHC/sJPxSKCIPq/JjAu+AzCvcKowVThC2FbhJs9S/jYDgwLSS0LflWxVKyBum9DLOL/3ohHxcjYQVtvGKw12nJX5hBsez0zbE29tIBz8RglPJatep8QIt4ksrD6f9NuHmFuXiWa/qgGsriJ2KwET/hh5jvX1ucSq4by2QphutnAomXWRNYUuBSRLh5jF7Tqz9nz+qCE/nRQVnpoicrsp4yl+JlNBvbqTrCw9GaY3BEkqYT6Cvf2/MTHF8i8rgVCA4EmyDFHUo0IVsLITJ8Q+Kf1/gKTzcoNdWPMh9IZIQFnEqcGQuTtCbJfmuLIVzlv2g6gXH8hjFcY67IWGFibZbXX+dsO0zauRk4Tzhk8I8wmcFrpfwIKFoohykHG40xyWWaJ6xRZT8usKbmhdxap8w4DHW+ycy3KfmLtqVr0rBvyI8rZBJudflTHUg9ImQySz+1BTv3zpR2RfiiRniG0b1aedxYaEMddsV/ZoKhH6ge0pDhYej/Aca0psdsqKBrt81y+yTtPeoHzMF+nmhkHTOlVW57K4Wwrk7quTWpkvfoxl0Hqmy46LylyoMdm2fQsfiKsMTzN0pysaLLKOD0M6v4hlt4jjKXIszCuDGNm20yg7XCbZf0KpgQt4wpVP36oT8NMmXqVCr/uMI0gYrYK3KvV/5eWS8KqF/zwyVe2mMdZvfOyJ+4Xh0Bo5D0ZOj+mNCQknhS5HeaUX1DZeC5yNldPLyogprUB9PixsZ/QlgFaaZrKREysxqlpkibT6VYakXHQzWMuVOKQv2/1nxuMPyrlgeg6yd7KwC6OIdj34UluhxvOjjbcL8QjdlCzUezl2a85PF1ukqnMWpiOvePGZXWPGK5zfGJ0XlcZKyCBNS6P+hGSp+IFYv1M8a3pWhvcaidXAqWC3O2udm5eEyj+RxKuLtbK6DYE8dx1i3+a2rUzE7Om93x09mUnxoUobSebJjKZQ35hGW8vcVzuGgxsKkyt75cU1sfCvKY0tgRJS/mcKwtRMlzQmeig4WVshE9Fp0nDaAWxySBQS2K8qSd0oR2zZBPq1I/IXPrUKGwjQXLvoQJqR+E5ytKwXGxFSBMZz1PKpKqRK2FVE6rFTNxZTdrOp/ENYWthBWEx4Smgl2TxDIv7RZgRZpcSc+zfgMqh5WpOhWat5Vx2BDt8NJMuDiFkZ8J8q7RGGze1qoCpfdkLqPsUkipZf5reKcLiilYdvjxbIaOF+Kgnf5vOJzZVDMFsCMEpDl5sPEcW8bG6coP/TpWy3K/jUqt2yLMklZ6A1tEI5OKpgx/SMxvb9sUhcnkPZYJWFAtJPDVIDyk9sVbJJ/mdLKOL9hCb5JE7mTGKdMePSNiXx1oQ6yoozAJnBRyQbhGOZdqcCU8UKw7ZskJMgXlU65vRPyWyU/o0zqcm1luZe00tmJvG3USODmghwNDovqX52jbtoqgdsD0lbIWC6MD1ab8krQAZe9Nsaq5vcOcRLG2OgcBJ8c1R+To25SlSUjndjF3NJWggcSCjJ5fjscROHnFT4XxXm6XyuKpwmGqhB7r0UxPE1jUZlVFXJCWt2w4k9gf2mhe3qUl9Wp2F719hPOiuneNBYvEo2vRJzaoIjzGSboWxXHsWgny0QFQl/blY/nc6Msem6pP29caUnxE6RnF+FNYTfhQaEOUteVCrj5oTAjImkvhYtE8XiwgA4mCo8LF8QzUsTXUJmlo3JhqTlFNRfpIwY8xnrrZL4jZm6qlYqhsQpEVxY+IRwohAkJRXgoEwSESSCt/FEFmVyLyhMZFOBUsGXx38INCfVWjKXfFYs3RpmI1hNwCH7fmJlwvJTSzxFOEpjYPi3g4KDjXIEJ9AzhcAFuOd5a4Gb9c+EfQisJTgWrRo1LnNgatjOujZRgy/nCTdFxY8D2D8KWUFahf62WC9Pqa3UO0uqIlxuvA56mkf2FG+bE6vHnJZmB18+YGF4Pk/5jBdf8d4VDBW4m3AsmC3HZVweM8QMEHLYswjUQhPE5t8CS/dHCk0KdpdVDSp3trpttHmPJZ6SOY4z7QBDmq8zyv6rBDe/jDTW/FqWTt1hDXt0Ofx3ZyhYIE3WjsL8+U6AvdwtM6kmyrTIod1VSAaXjmG0n4JDRHu3fLpCOMFmj4xmBNFaCfiWEAXSl4uQDJtdWE83qsbJTFG+ULygh6FpP8WOFR4RmT5xKnvNeyVsKnxK4wfeDjFMnXhfg4Rs17RCrFdh3T8n2TZe+Rwvq5PrAWcC+vwjxccG18rjAWG52bSm5peBAhPE5UnEcljuFcK0oWlvZW5YF2y/JYeWwqP5g3/6Aul4dY4x7xgAOdRUyTUrDGFsrRwMnR/XL3P7gQSDYdFAOm4ZMihRMVciJR3jyZWJCcbOJTMm1Ep7gAwlM6BsJ3LS4IW4jcKMkH495TaGVzKPMp4WXhKQbH09uob2XFaf9FYQgxysS8tE1Qwj53LDDBBjKfFhpSRJ3GrZvUohJNOi5VXHsXrtJuZC0uyKUPzEk9HiI0xUm7MsUD45bp7rFRZ1mwnlM5eD92ZINmy59RZ0KTKIPYRztQEIk+ygkPawChfS0Ieck6P2N4i8KK6et3MVyK6pt7iXBdq7xVTPaMyyqb6digLheHGNVORXMM/F7O+OMewlzVhahDnXLdCrCNY9e4pnlPNWYEYEJiQufSY8nF16qWUios7A1Q+cvFtiyYZLnGAfitSjO8c3CakIa+boKUWevhMJhYqYMN8mNG8q9W8ehbSY8PL+4YCt1AybFMxviP4nKsUWyYEMeh9sKbwnoekrYRGgl1yuTsmu3KtQjeUvITiZU+vM7odNjdRW1ybWSNE6U9R/BvnC+R/wntXikLKdis5h9YYsNB/hhgfvDMCGPHKxKod/YumEeJR2ss5zaelII11SwnZC0qcJ+QhqBM+rZqRhgqxfHWBVOxQmiY1Y0NuLjizhz8ANCWjlZBak3Jm2FFOXC/IfenVKUf1uRLZWyfJQ6SuF2Aief1YpeEJyK8TFD51d8a+EQ4WvCXsI6wlxCWhmlgpxcVjiGCs2Em+NWQtJExhu0OwhMfM2ECeljAiduj2YFMqStqbI4Ns2cjriazXVAezgqvS4LqAO3CfTnCWEZoZPCuPu9MFNIGgNxe76rA2wFY4WyhIm6jJUK7GH7MNi4uuKsoHE8SSgirByOExYuoqQH63bCqeBBgnN0QEX8jI/071mS/l4bY1XzW5TWKpyKK6JzzrhK+yBetB+Dov6uEbFcVFUJ71o8LwyvqoEGvbfoGEepU+01NF/aIQ7iRQKDnkm906suS6nN+6L2cRbSyL4qhL1lTwBlOhVxG8+SrUwArPzhQFmyM9AJp2JVmcXqZFVOddlORa+Nsar5zT6q/n+NKpwKVie5TzE3WUpmgBPGTXXdkvWyrDxZYEtjx5J1J6n7ijJeE9ZPKtBD6UfLVgb9m8K2HbR7ebV1koAjExyE96Vsf41YHSbssqRMp4KVrheE0DfCE8sydBDq6YRTUTWtZTsVHmPlnrGynYr5ZN4bAtf+5eWaam0wMFS4VWAJjAmlLPmUFE0TynZWkuwL2yxVLZEmtVtFOsuwYdLrVH/WUpvfF3h/IrRN+GchrbC68jeBeoypsqRMpwKbjhdCH19VvKonYNrqd7FT0fwMe4w15yVPatlORfzhZ2Ieg1ynPQMjVOQ3Asvd87QvnqoE2w+dWlLmSfqfwlGpLKt3Id71YbWFSe/0kkxlsmevny2NFQW2UnYWvixcJNwvhEm2MTxceVnkFyqMDpyLsqRsp2KkDGMFCDu/VZaRg1SPnYrmJ95jrDkveVLLdip2lRHhPrdBHoNcJx0DLAntJrBt0Wuyqgxmz7XXZWV1IL40j6PE9lERvKL6bwnhIsoSzla9rKtXR8XaylpXVZtK2U4FjZwvPCNw87fkZ8BORTJ3HmPJ3GTJKdupOEONcx+cJbBSn0pSF0ylbXAUYtn7kh7tKi/d9Losqg5cLbwz1pH5Y/FuRK9To0zoWeT2WOGtFP9e7LhO0T3rZIxt6UsGPMbqeVrDO2q/lXmsWKaSXnzaTtUxF+pbBj6kno2uWe/Oy2EPFypPAcguA4H/mgEzYAZqwQCfj7IFjGR678tOxQBp/ts7DJwnU3mfhfcf6oIfyZas8pIq/D6qtIVClsctZsAMmIE6MBBWKbDFTkUdzohtMAMpGOC3SRC2b7abE/MfM2AGzED3GQhOxYsy5ddZzPFKRRa2XNYMlMvARVLHRYt4C2SAB/81A2aguwywarppZMIPFPKVXWqxU5GaKhc0A6UzwG8/nBNp/aBCfm7cYgbMgBnoJgO8t8ZXjsjZA0H6v3Yq0nPlkmagCgb4/Qc+ZX2HgGNhMQNmwAx0k4GJUeP8JtOfshpipyIrYy5vBsplYJrU/SxSeWi5qq3NDJgBM5CJgS1VOvy685RMNaPCdirysOY6dWeA37IIe4Jl2Lq6lHxfWKwMZU108CMzyIaCX9icQ4X/mAEz0AUGDo7afFThhXnat1ORhzXXqTsDvKdwi1D010P55c4LhAeEvYSqfmTreukOP0z2VcUtZsAMmIFOM7COGuSH+JAjhDfmxDL+GZqxvIubgV5g4AkZ+bLAT28XkXGqzC9d8mXGgkUUtanLj2AdIlwprC/sJFwhWMxAHRmYJKMOSDDsVKXzVZOlGgYmSW3Su1erFGwyrFLw+zk/KajL1c1A3zFQpsP8iNhh4l+6YpZwYGjnXoEf9soqvFSV+cWqrI24fC4G+EyP/1FzWa7a9ai0R9QH+pGET9XD1L61gv/vkcR9SH9vjt5voDr8FDf3nw/kqO8qZqDvGZi3xB52yqkYLpunCVzYHxYsZsAMmIGqGeBT9gcF7jteZaqabevvKQYmydpfCNOFbwtlSaecCuwdK/CJ6XPCkoLFDJgBM1AlA6x+4FBMFRapsiHrNgO9xgAe91UCF8hukfHnKuT9irRotkLQSacCsycL9OEaDixmwAyYgYoY4Cu52cIb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width=\"266.5\" height=\"46\" style=\"width: 266.5px; height: 46px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            where: the symbol \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAmCAYAAABUKMJkAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAL6ADAAQAAAABAAAAJgAAAADlRKSGAAAA/ElEQVRYCe2YPQrCQBSE4x9YaG8teAXxEp7AO0hu4xWsbTyDWHkPK8VO1Fmw2qx5m+dIECawxc6bN/vyJdUWhR4REIGYwBbCKhZ/uJ8i+4A1YZxxRciGEZSZsYTviTW3/F3LgHrnvTKsVMvQSssZ3spora7h20Iv8iLvIKDfxgGN0iLyFIyOEJF3QKO0iDwFoyNE5B3QKC0iT8HoCBF5BzRKi8hTMDpCRN4BjdLy1+T7mQgG8I0ib7iSu0Va0224FYtnGDcNqfOfUQyDpta+rtGolag/PuSGsxZGf+WtU/41xFmicId2TOi50g7G8DV7iYYLtFNClyQC3xJ4ASZiG5LKUdtBAAAAAElFTkSuQmCC\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" and \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" are the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/floor.html#\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003efloor\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/ceil.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eceil\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e functions, respectively.\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAkCAYAAAANdf2OAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAWKADAAQAAAABAAAAJAAAAADbokXeAAAEaUlEQVRoBe2Ya4iWRRTHt9J0zUhUzEsXgtVERAOpRWFTUMrUxLT8UN5FCkS0MhHFvqalfREiAovqSze60GqEWiKS9iHFD6KIuizrqlHWouUFL/X76xw5Ps6z7/usQa+7c+C3c+bMmXlmzjNzntm3qipJikCKQIpAikCKQIpAikBbInBbWzrdwn36M/cBkfkrDrUwAZ6KtMvUD56FGrgEW2AbnIEkIQI7Kf9phYU5kVqE/Txchm3wE2icczALkhCBOmgtuKdovzsSqfnYFFgx1rVPRNd42s0znP06tSOliG9Z+Xh4ExSUrGzCsCtjHEf9e7gd3oMXwcsGKvNA4z0Ke6BDyhBWrR34ccHV1+Nvu35gpO8g165gd1h5n5UrUPpIlXtq9VG7GPodo8yTEzRobH3seuY5tWe7bg76QNlOPImudDET7oI8WUqD9fkkzwn7Z87vho+kcktrUk3j0/A6rITu4OVJKm/BZG+sMH0x87nTzUm7bBJ8BE3wPMRkmDPud3pW3ecMg51eUl2Dx2lQArc3udb1Wufsf6F3c22VpL7KZH4GrcXWkS1XRSa81fnrJeXJEhpsvG/ynGJ2JXDt2PtAAdQg9iZfDjbltiOwGcqRL3HSEb1Z/HWpnOfKR7n3AZgFDWBBsXIqNi9aq7XN9g0ZfY7za/Mt4is3yBPoumArPRQVvQib9M2U44s+OOPfhfoy8Ln5AHWfMv+kbnOcgp4n02gwv+asU6esIae+Hbs9RPdCpQqVRWU1HT4v2ini/0vEVsSkwOo+rLTxTuj4MOUo2BHqZyl7BL21m4eP4R3Bv3BRSw97S43olZpvCy+MDp+6tb3gBtBxtzXPcfasqjbz25tt9Eci2+brepjSgkS7R3e+9iJfuIX0cfqvTred7EzXVN92/Jo1KOUGWMdAHzrJyKtFu/m7262kxelHne6D6MxXVN92wz8kPn9kO/q6cm7vYOhLWQOHQr1IoVvE6CIdcnynY9c16r8QO5kay+/A76jPDw8YHspY4e/LP8YcStkm4aC7sD4GlmvmluqU014ptwg/vQlhXbo1VLsG6XY9/R099qGTTVdOxeVv6A7XSakdfC/eG0A7WDeAl0CD1sEH0BnWwwr4A0pJpdwi/DxfCZUPKXVzMJG+EXRaeoF2avYj9gg2+/3ha3RLo6hxUcAngn456go7YCfYi9AD9LZ0lGR7F36A2NvF/L+L/g1uAP07q98Jst+cBdi0ngPgP3BUr4jiYDu0Pth8oTSi/i0w1Dfk6co56iB0R/wNHgSTN1CsXQldD/ft5lcppXK+zVelNsvjMALeBtkOQn/Ik9E06N4s39egS2B5sCmHj4Gy5Dm8NJDQkc/eGB7CZg9TzlKqqGR5jMk1g63Jl7IvgXLu9M/g1xjG0bqFxpJtMuRK7GjX4n0PKD2cifTUUZLPLtAOr3TpzAS1Ue4HBbMJGuAIXIByRePohdWEDocpFQP9ZpwkRSBFIEUgRSBFIEUgRSBFIEUgRcBF4F+kFEMm9jjRjQAAAABJRU5ErkJggg==\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; 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 40px; transform-origin: 404px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; 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 10px; transform-origin: 404px 10px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  S = @(x,n) sum(arrayfun(@(i) ceil(nthroot(i-1,n))+floor(nthroot(i+1,n)),1:x));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; 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 10px; transform-origin: 404px 10px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(50,3)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; 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 10px; transform-origin: 404px 10px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; 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 10px; transform-origin: 404px 10px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        279\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(x,n)\r\n    s = sum(arrayfun(@(i) ceil(nthroot(i-1,n))+floor(nthroot(i+1,n)),1:x));\r\nend","test_suite":"%%\r\nx = 50; n = 3;\r\ns_correct = 279;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 100; n = 2;\r\ns_correct = 1339;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 1000:2000; n = 4;\r\ns = sum(arrayfun(@(i) S(i,n),x));\r\ns_correct = 15056572;\r\nassert(isequal(s,s_correct))\r\n%%\r\nx = 1234; n = 5;\r\ns_correct = 8508;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 10000:20000; n = 6;\r\ns = sum(arrayfun(@(i) S(i,n),x));\r\ns_correct = 1271494600;\r\nassert(isequal(s,s_correct))\r\n%%\r\nx = 123456; n = 7;\r\ns_correct = 1164369;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 100000:200000; n = 8;\r\ns = arrayfun(@(i) S(i,n),x);\r\nss = floor([mean(s),median(s),mode(s),std(s)])\r\nss_correct = [1205294 1205294 755294 259811];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nx = 1234567; n = 89;\r\ns_correct = 3703698;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 123456789; n = 10;\r\ns_correct = 1462257359;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 1234567891011; n = 12;\r\ns_correct = 23191068638973;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 11111111111111; n = 111;\r\ns_correct = 33333333333330;\r\nassert(isequal(S(x,n),s_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-05-08T15:29:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-08T10:48:38.000Z","updated_at":"2023-05-08T15:29:34.000Z","published_at":"2023-05-08T15:28:45.000Z","restored_at":null,"restored_by":null,"spam":null,"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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a postive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following summation:\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\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es= S(x,n) = \\\\sum_{i=1}^x \\\\bigg(\\\\Big\\\\lceil \\\\sqrt[n]{i -1} \\\\Big\\\\rceil+\\\\Big\\\\lfloor \\\\sqrt[n]{i+1} \\\\Big\\\\rfloor\\\\bigg)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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                            where: the symbol \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" and \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lceil\\\\ \\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" are the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/floor.html#\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/ceil.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e functions, respectively.\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 example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\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[\u003e\u003e  S = @(x,n) sum(arrayfun(@(i) ceil(nthroot(i-1,n))+floor(nthroot(i+1,n)),1:x));\\n\u003e\u003e  s = S(50,3)\\n\u003e\u003e  s =\\n        279]]\u003e\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":58274,"title":"Easy Sequences 116: Summation involving nthroot, floor, and ceiling functions","description":"Given a postive integers  and , we are asked to evaluate the following summation:\r\n                            \r\n                            where: the symbol \"\" and \"\" are the floor and ceil functions, respectively.\r\nFor example, if  and , we have:\r\n\u003e\u003e  S = @(x,n) sum(arrayfun(@(i) ceil(nthroot(i-1,n))+floor(nthroot(i+1,n)),1:x));\r\n\u003e\u003e  s = S(50,3)\r\n\u003e\u003e  s =\r\n        279","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; 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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 226px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 113px; transform-origin: 407px 113px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a postive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; 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 23px; text-align: left; transform-origin: 384px 23px; 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\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"266.5\" height=\"46\" style=\"width: 266.5px; height: 46px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            where: the symbol \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" and \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" are the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/floor.html#\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003efloor\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/ceil.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eceil\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e functions, respectively.\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" style=\"width: 44px; height: 18px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; 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 40px; transform-origin: 404px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; 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 10px; transform-origin: 404px 10px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  S = @(x,n) sum(arrayfun(@(i) ceil(nthroot(i-1,n))+floor(nthroot(i+1,n)),1:x));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; 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 10px; transform-origin: 404px 10px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(50,3)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; 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 10px; transform-origin: 404px 10px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; 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 10px; transform-origin: 404px 10px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        279\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(x,n)\r\n    s = sum(arrayfun(@(i) ceil(nthroot(i-1,n))+floor(nthroot(i+1,n)),1:x));\r\nend","test_suite":"%%\r\nx = 50; n = 3;\r\ns_correct = 279;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 100; n = 2;\r\ns_correct = 1339;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 1000:2000; n = 4;\r\ns = sum(arrayfun(@(i) S(i,n),x));\r\ns_correct = 15056572;\r\nassert(isequal(s,s_correct))\r\n%%\r\nx = 1234; n = 5;\r\ns_correct = 8508;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 10000:20000; n = 6;\r\ns = sum(arrayfun(@(i) S(i,n),x));\r\ns_correct = 1271494600;\r\nassert(isequal(s,s_correct))\r\n%%\r\nx = 123456; n = 7;\r\ns_correct = 1164369;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 100000:200000; n = 8;\r\ns = arrayfun(@(i) S(i,n),x);\r\nss = floor([mean(s),median(s),mode(s),std(s)])\r\nss_correct = [1205294 1205294 755294 259811];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nx = 1234567; n = 89;\r\ns_correct = 3703698;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 123456789; n = 10;\r\ns_correct = 1462257359;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 1234567891011; n = 12;\r\ns_correct = 23191068638973;\r\nassert(isequal(S(x,n),s_correct))\r\n%%\r\nx = 11111111111111; n = 111;\r\ns_correct = 33333333333330;\r\nassert(isequal(S(x,n),s_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-05-08T15:29:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-08T10:48:38.000Z","updated_at":"2023-05-08T15:29:34.000Z","published_at":"2023-05-08T15:28:45.000Z","restored_at":null,"restored_by":null,"spam":null,"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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a postive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following summation:\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\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es= S(x,n) = \\\\sum_{i=1}^x \\\\bigg(\\\\Big\\\\lceil \\\\sqrt[n]{i -1} \\\\Big\\\\rceil+\\\\Big\\\\lfloor \\\\sqrt[n]{i+1} \\\\Big\\\\rfloor\\\\bigg)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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                            where: the symbol \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" and \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lceil\\\\ \\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" are the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/floor.html#\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/ceil.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e functions, respectively.\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 example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\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[\u003e\u003e  S = @(x,n) sum(arrayfun(@(i) ceil(nthroot(i-1,n))+floor(nthroot(i+1,n)),1:x));\\n\u003e\u003e  s = S(50,3)\\n\u003e\u003e  s =\\n        279]]\u003e\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\"}]}"}],"term":"tag:\"builtin 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