(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**