Help Solving Series Related to z = rexp(ix)

[bodensee9]

Homework Statement

Hello, I am wondering if someone can help with the following. I am supposed to show that

Series from n = 1 to inf r^n*cos(nx) = rcosx -r^2/(1-2*rcosx + r^2). I am supposed to relate it to the fact that z = rexp(ix). I know that this expression is the real part of z^n or r^n*exp(inx). But I'm not sure what to do after that?

Any hints would be greatly welcome! Thanks!

Homework Equations

The Attempt at a Solution

 

[Dick]

Written in exponential form it's a geometric series. Sum it.