Fourier Example

Find the Fourier Series of the function:

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

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