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

1084 Solutions
68 Solvers

Last Solution submitted on Dec 27, 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

Problem Recent Solvers68

Problem Tags

infinite series

Problem 415. Sum the Infinite Series

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers68

Suggested Problems

More from this Author3

Problem Tags

Problem 415. Sum the Infinite Series

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers68

Suggested Problems

More from this Author3

Problem Tags

Players