(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [itex]f(x)=x[/itex] on [itex] [-\pi,\pi) [/itex] and peridically extended. Compute the fourier series and hence show:

[itex] \sum_{n \geq 1,nodd} \frac{1}{n^2} = \frac{\pi^2}{8} [/itex] and [itex] \sum_{n \geq 1} \frac{1}{n^2} = \frac{\pi^2}{6} [/itex]

2. Relevant equations

Parseval's equality

3. The attempt at a solution

I computed the fourier series to be [itex] -\sum_{n=1,nodd} \frac{4}{n^2 \pi} e^{inx}+\frac{\pi}{2} [/itex] (even terms [itex]\hat{f}(n)=0 [/itex]) and proved the first sum (letting x=0).

How would I compute the second part? how do i get the whole sum from this? I tried to slipt the sum into even and odd parts, but i dont know how to compute the even sum when I dont have any terms for the even sum! thanks

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# Homework Help: Fourier Series - proving a sum

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