Computing a power series

1. Oct 7, 2009

quasar_4

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

Compute $$\sum_{n=0}^{\infty} p^n cos(3nx)$$ for $$\abs{p} \textless 1$$, where $$p \in \mathbb{R}$$.

2. Relevant equations

3. The attempt at a solution

I was thinking that maybe this could be approached as a telescoping series, but I'm not really sure if it is. Would that be the most expedient approach? Clearly it isn't geometric, and I'm not sure how to find the sum of a general power series.

2. Oct 7, 2009

quasar_4

No one? Someone has to know. There are a lot of clever people on this forum.

3. Oct 7, 2009

quasar_4

What if I rearrange it using the fact that cos(3nx) = 1/2(exp(3nix)-exp(-3inx)). Could I then write $$\sum_{n=0}^{\infty} (pe^{3xi})^n + \sum_{n=0}^\infty (pe^{-3ix})^n$$ and try to work from there? (ie, is that valid?)

4. Oct 7, 2009

quasar_4

Ok, I was being silly, as usual - it is actually geometric after all.

Thank you to me for figuring out this problem.