(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove the following identities:

[tex]\sum_{n=0}^{\infty} r^n \cos(n\theta) = \frac{1-r\cos(\theta)}{1-2r\cos(\theta)+r^2} [/tex]

[tex]\sum_{n=0}^{\infty} r^n \sin(n\theta) = \frac{r\sin(\theta)}{1-2r\cos(\theta)+r^2} [/tex]

2. Relevant equations

[tex]\cos(n\theta) = \frac{1}{2}(e^(in\theta)+e^(-in\theta))[/tex]

3. The attempt at a solution

I get it to this point...

[tex] \frac{1}{2}( \sum_{n=0}^{\infty}(re^(i\theta))^n+\sum_{n=0}^{\infty}(re^-(i\theta))^n[/tex]

But I dont know what to do next! r could be less than or greater than one. I need to do the general case where r could be either....

Also, Im not sure that the 'relevent equation' is really relevent

Any help/tips would be greatly appreciated, Thx!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Prove sum identities

**Physics Forums | Science Articles, Homework Help, Discussion**