# Thread: Fourier series to calculate an infinite series

1. ## Fourier series to calculate an infinite series

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?

2. 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.