How can I use Fourier series to solve for f(x) when given specific conditions?

[gtfitzpatrick]

Homework Statement

if 0<[tex]\lambda[/tex]<1 and
f(x) = x for 0<x<[tex]\lambda\pi[/tex] and
f(x) = ([tex]\lambda[/tex]/(1-[tex]\lambda[/tex]))([tex]\pi[/tex]-x) for [tex]\lambda\pi[/tex]<x<[tex]\pi[/tex]

show that f(x)= 2/([tex]\pi[/tex](1-[tex]\lambda[/tex]))[tex]\Sigma[/tex](sin( n[tex]\lambda[/tex][tex]\pi[/tex])sin(nx)(/n[tex]^{}2[/tex]

Homework Equations

The Attempt at a Solution

am i right in saying that there is only odd so ao = 0 and an = 0

and bn = 2/[tex]\pi[/tex]

 

[lippyka]

\Sigma[sin(n\lambda\pi)sin(nx)/n^2]and so f(x) = 2/(\pi(1-\lambda))\Sigma[sin(n\lambda\pi)sin(nx)/n^2]