# How to show this convergence?

1. Apr 28, 2015

### Mr. Rho

1. The problem statement, all variables and given/known data

I need to show that $\sum\limits_{n=0}^\infty \frac{sin^{4}(\frac{n\pi}{4})}{n^2} = \frac{\pi^{2}}{16}$

2. Relevant equations

I have this property for odd n

$\sum\limits_{n=0}^\infty \frac{1}{n^2} = \frac{\pi^{2}}{8}$

3. The attempt at a solution

I have no idea how to do this, any help?

2. Apr 29, 2015

### haruspex

There are only so many values that $\sin(\frac{n\pi}{4})$ can take. How about splitting the sum up on that basis?