Originally Posted by

**Deadstar** Ugg this is driving me mad...

Consider the function $\displaystyle f : [-\pi, \pi] \rightarrow \mathbb{C}$ defined by $\displaystyle f(\theta) = |\theta|$. Use Parseval’s Identity to prove

$\displaystyle \sum_{k=0}^{\infty} \frac{1}{(2k+1)^4} = \frac{\pi^4}{96}$ DONE

and also

$\displaystyle \sum_{k=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90}$

Ideas...

I thought since it doesn't say you HAVE to use the $\displaystyle |\theta|$ function (which I used for the first part) than I could do the second part using $\displaystyle f(\theta) = \theta^4$ but that didn't work as Parsevals complicated things way too much.

So I thought maybe find a sum for all the even terms? Like, find $\displaystyle \sum_{k=0}^{\infty} \frac{1}{(2k + 2)^4}$