okay, so i was given the piecewise function f(t)= k if -pi/2< x< pi/2

0 if pi/2 < x < 3pi/2

i computed the series to be

$\displaystyle Sf(t)= \frac{k}{2} + \sum_{n = 1}^\infty\frac{2k}{(2n-1)\pi } {(-1)}^{ n+1} \cos((2n-1)t)$

which i think is right,

but now i need to show that $\displaystyle \frac{\pi}{4 } = [1-1/3+1/5-1/7+........] $

i know it is probably pretty simple but iam a bit stuck so what steps should i take to show this.