Problem 415. Sum the Infinite Series

Created by Roger Stafford

Solve Later

Given that 0 < x and x < 2*pi where x is in radians, write a function

 [c,s] = infinite_series(x);

that returns with the sums of the two infinite series

 c = cos(2*x)/1/2 + cos(3*x)/2/3 + cos(4*x)/3/4 + ... + cos((n+1)*x)/n/(n+1) + ...
 s = sin(2*x)/1/2 + sin(3*x)/2/3 + sin(4*x)/3/4 + ... + sin((n+1)*x)/n/(n+1) + ...

Solve

Solution Stats

1047 Solutions
64 Solvers

Last Solution submitted on Nov 18, 2019

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

James on 15 Mar 2012

So what would the Cody size of a brute-force algorithm be for this problem?

David Hill on 7 May 2018

I got the correct answers within 50*eps for all answers except x=0.001 for c. Is c_correct value correct for x=0.001? I put in a small correction factor 1.5e-14 to get your c_correct value.

Solution Comments

Solution 53910

2 Comments

2 Comments

bainhome on 16 May 2018

this one is truely a wonderfun code! make my eyes open.

Augusto Mazzei on 19 Sep 2019

Mr Castanon is a true god. I preferred asking wolfram solver.
Wish I studied infinite series properly at school

Solution 51711

2 Comments

2 Comments

Roger Stafford on 26 Feb 2012

Yes, you are right S L, a direct brute force summation is surely not the most efficient method of determining the sums of these series. You are the only one so far with a valid solution that met the 50*eps tests. In fact your answers are very much closer than that to mine, within a few eps. However, there is another single analytic function that can be used which is much simpler and would undoubtedly give you a lower "size" than 92 if you or others can find it. R. Stafford

@bmtran (Bryant Tran) on 28 Feb 2012

thanks for the hint

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Problem 415. Sum the Infinite Series

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Problem 415. Sum the Infinite Series

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