Fourier series to calculate an infinite series

**arbolis** · August 4th 2010, 01:36 PM

I'm not asking the solution, but rather the main idea of how to solve the part 2:
1)Find the Fourier development of $f(t)=|t|$ with $-\pi \leq t \leq \pi$ .
2)Show using the previous result that $\sum _{k=0}^{\infty} \frac{1}{(2k+1)^2}=\frac{\pi ^2}{8}$ .
Attempt: Is it just by using Parseval's theorem?

**chiph588@** · August 4th 2010, 01:49 PM

Originally Posted by arbolis

I'm not asking the solution, but rather the main idea of how to solve the part 2:
1)Find the Fourier development of $f(t)=|t|$ with $-\pi \leq t \leq \pi$ .
2)Show using the previous result that $\sum _{k=0}^{\infty} \frac{1}{(2k+1)^2}=\frac{\pi ^2}{8}$ .
Attempt: Is it just by using Parseval's theorem?

I do believe you could use Parseval's theorem for part 2.

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