Proving Fourier Series of f(x) for 0<\lambda<1

[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 = 1/[tex]\pi[/tex](integration of the 2 parts)(sin nx)

 

[kurt.physics]

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