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

Show that: [itex]\sum_{n=1}^{\infty}\frac{1}{n^4} = \frac{π^4}{90}[/itex]

Hint: Use Parseval's theorem

2. Relevant equations

Parseval's theorem:

[itex]\frac{1}{\pi}\int_{-\pi}^{\pi} |f(x)|^2dx = \frac{a_0^2}{2}+\sum_{n=1}^{\infty}(a_n^2+b_n^2)[/itex]

3. The attempt at a solution

I've been trying to solve this for ages and I just can't figure out what to do. I know you're supposed to use Parseval's theorem. All I've managed to do was plug in [itex]\frac{1}{n^4}[/itex] into the summation part of the Parseval's equation and I substituted the formula for a_{0}but I couldn't get very far.

Any help would be really appreciated.

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# Homework Help: Evaluate infinite sum using Parseval's theorem (Fourier series)

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