
Fourier series
Quick Q.
When dealing Fourier series Q's, $\displaystyle \cos(n \pi)$ is written as $\displaystyle (1)^n$. What can $\displaystyle \cos (\frac{n \pi}{2})$ be written as? I might as well write out the equation i'm trying to simplify...
$\displaystyle \frac{2T}{n \pi}( 2 \cos \frac{n \pi}{2}  1  \cos{n \pi} )$ = ?

its either 1,0, or 1
if n is odd it is 0
If n is even its either 1 or 1
So there is no simple form

Cheers, think I've got it figured out anyway...
It equals $\displaystyle \frac{8T}{n \pi}$ whenever n is in the form 4m + 2 and 0 otherwise.