Find the sum of the first n

Find the sum of the first n terms of the harmonic series where n is an integer greater than one 1+1/2+1/3+1/4+1/5+.....

[Yogesh]

Consider the following divergent infinite series:

S=1/2+2/3+3/4+⋯+n/n+1

Write a MATLAB code that takes a value of n and returns S.

Please report the values below: Please report the value of S for n=10

Answer 1

[John Chilleri]

Hello,

This can be done simply with,

n = 100; % whatever you want
sum_harm = 0;
for i = 1:n
   sum_harm = sum_harm + 1/i;
end

or even,

n = 100; % whatever you want
sum_harm = sum(1./(1:n));

Hope this helps!

[bassam792]

it's wrong

[John Chilleri]

Did you change the n to your desired value?

[John Chilleri]

There is a built-in harmonic function, but I wasn't sure if you wanted to write your own,

harmonic(n)

is the built-in MATLAB function, which should agree with both above.

Hope this helps!

[John Chilleri]

Fixed my code - I was using a variable named sum, which can cause errors with an unclear workspace, I apologize.

[Marvin Jones]

What if you wanted to go in reverse say from n to 1?

[Walter Roberson]

The theoretical sum would be the same. If you are using floating point then the result could differ. The order of operations of built-in functions like harmonic() is not specified. For doing it yourself, replace 1:n by n:-1:1

[Walter Roberson]

format long g
n = 1e10; % whatever you want
sum_harm_forward = 0;
sum_harm_reverse = 0;
for i = 1:n
   sum_harm_forward = sum_harm_forward + 1/i;
   sum_harm_reverse = sum_harm_reverse + 1/(n - i + 1);
end

sum_harm_forward

sum_harm_forward = 
          23.6030665949975

sum_harm_reverse

sum_harm_reverse = 
          23.6030665948883

sum_harm_forward - sum_harm_reverse

ans = 
        1.092317347684e-10

Answer 2

[Roger Stafford]

Or how about this one-liner:

H = det(diag(2:n)+ones(n-1))/factorial(n);

inspire by http://oeis.org/A000254.

[Ahmad Taheri]

hi ,admin

one qustions

∑1/n=?

∑1/n^2=??

[Walter Roberson]

∑1/n is infinite.

∑1/n^2 is pi^2/6

Answer 3

[Walter Roberson]

syms x n
symsum(1/x, x, 1, n)

[Hesbon Osoro]

Very much useful to test the convergence of a harmonic series without lagging a machine, so fast code also. It is of great help.

Answer 4

[Vaibhav]

the examples in the course videos have been about convergent series. In this example, you will code a series that does not converge: S=1+12√+13√+⋯+1n√

Write a MATLAB code that takes a value of n and returns S. Please report the values below:

Please report the value of S for n=10

Please report the value of S for n=100

Please report the value of S for n=500

[Walter Roberson]

Is that the sum of 1 + 1*x^(1/2) + 1*x^(1/3) ... + 1*x^(1/n) ?

Is it the sum of 1 + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(n) ?

format long g
syms n m
S = 1 + symsum(1/sqrt(factorial(n)), n, 2, m)

S = 

double(subs(S, m, [10 100 500]))

ans = 1×3

2.46928512326805 2.46950631452105 2.46950631452105

Answer 5

[Yogesh]

Consider the following divergent infinite series:

S=1/2+2/3+3/4+⋯+n/n+1

Write a MATLAB code that takes a value of n and returns S.

Please report the values below: Please report the value of S for n=10

[Steven Lord]

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the free MATLAB Onramp tutorial to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.