Fourier Example

Find the Fourier Series of the function:

$f(x)={\begin{cases}0,&-\pi <x<0\\\pi ,&0<x<\pi \\\end{cases}}$

$b_{n}={\frac {1}{2}}{\pi }\int _{0}^{\pi }\pi \sin(nx)\,dx,={\frac {1}{n}}(1-cos(x\pi ))={\frac {1}{n}}(1-(-1)^{n})$