I have some problems which says show that(adsbygoogle = window.adsbygoogle || []).push({});

(i) [tex] \sum_{n=1}^\infty \frac{1}{n^4} = \frac{\pi^4}{90} [/tex]

and

(ii) [tex] \sum_{n=1}^\infty \frac{(-1)^{n-1}}{n^2} = \frac{\pi^2}{12} [/tex]

And another one which says, show that for [tex] 0<x<\pi [/tex]

[tex] sin x + \frac{sin 3x}{3} + \frac{sin 5x}{5} + ... = \frac{\pi}{4} [/tex]

The problem is that, the function I am supposed to work with ([tex] f(x) [/tex]) is not given. So I want to know if there is some way to find out which function I should start out with to achieve the results.

If I know f(x), I can write it as a fourier series and then substitute values of x to get the numerical series. But without knowing what f(x) to start with, I am stuck.

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

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!

# Homework Help: Evaluation of Numerical series by Fourier series

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