# Sine fourier series

1. Feb 21, 2010

### EmmaK

1. The problem statement, all variables and given/known data

Find a sine Fourier series for the function f(x)=1 define on 0<x<1. use this series to show that $$\Sigma\stackrel{(-1)^k}{2k+1}$$ =$$\stackrel{\pi}{4}$$ betwen k=0 and infinity

2. Relevant equations

3. The attempt at a solution

i found the fourier series to be$$\Sigma$$ ($$\stackrel{2-2cos(n)}{n}$$)(sin(nx)) between n=1 and infinity but don't know where to go form here.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution