To find the sum of a fourier series ?

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Homework Help Overview

The discussion revolves around finding the sum of a specific series related to Fourier series, specifically the series defined by the terms ((-1)^(n+1))/(2n-1) from n=1 to infinity. The original poster expresses uncertainty in their approach and seeks assistance.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Some participants question whether the goal is to find the sum of the series or merely to demonstrate its convergence. Others suggest exploring connections to Taylor series or logarithmic functions.

Discussion Status

The discussion is ongoing, with various approaches being considered. Some participants have offered alternative perspectives on the nature of the series, indicating a productive exploration of the topic.

Contextual Notes

There is a noted distinction between Fourier series and power series, which may influence the direction of the discussion. The original poster's request for clarity suggests potential gaps in their understanding of the concepts involved.

cabellos
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to find the sum of a Fourier series...?

My problem is:

I must find the sum of ((-1)^(n+1))/2n-1 between infinity and n=1.

I have looked in all my available textbooks for a clear example but I am still unsure as to how i should approach the problem?

Help with this would be much appreciated.

Thankyou.
 
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Do you really have to sum it, or just show it converges? The former is easy. I'm not sure how to do the latter unless someone can think of a taylor series that resembles your series.
 
Try this. Take the series for log(1+x) and think about putting x=i.
 
But that's not a "Fourier series", that's just a power series.
 

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