# Fourier Series- half range sine series

1. Nov 6, 2012

### Kamekui

1. The problem statement, all variables and given/known data
Let f(x)=x, 0≤x≤p

(a.) Compute the half-range sine series
(b.) Use the series to show that 1-(1/3)+(1/5)+...=π/4

2. Relevant equations

bn=(2/L)*int(from 0 to L) f(x)*sin(nπx/L) dx

3. The attempt at a solution

bn=(2/p)*int(from 0 to p) x*sin(nπx/p) dx

Using integration by parts I get:

bn= 2[(-p*cos(nπ)/nπ) + (p*sin(nπ)/n2π2)]

I'm not really sure where to go from here, any help is appreciated.

2. Nov 6, 2012

### vela

Staff Emeritus
Since n is an integer, you can simplify $\cos n\pi$ and $\sin n\pi$.