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

[gtfitzpatrick]

Homework Statement

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

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

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/$$\pi$$

 

[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]