Find the fourier series for

$\displaystyle f(x) = \left\{\begin{array}{c l} 0 & -\pi < x < 0 \\ 1 & 0 < x < \pi \\ f(x + 2\pi) & -\infty < x < \infty \end{array}\right.

$

By considering the Fourier series at $\displaystyle x = \frac{\pi}{2} $ show that $\displaystyle \frac{\pi}{4} = \sum_{m=1}^{\infty} \frac{(-1)^{m+1}}{(2m-1)}$

I am not enjoying these at the moment. I get lost. Really lost. (Angry)