# Homework Help: Finding the sum of an infinite series

1. Jun 22, 2011

### waealu

1. The problem statement, all variables and given/known data
I am supposed to find the value of the infinite series:

$$\sum_{n=0}^{+\infty}\frac{\pi\cos(n)}{5^n}$$

2. Relevant equations

I asked this question before on this forum and micromass told me that I should use cos(n)=((e^i)^n+(e^(-i))^n)/2. That equation worked and I was able to find the correct answer. I used that equation to find a "a" and an "r" in order to find the solution using =a/(1-r).

But my instructor said he would like me to try and solve it by only using real numbers.

How would I start to solve that without the imaginary numbers?

Thanks

Last edited: Jun 22, 2011
2. Jun 22, 2011

### lanedance

just an idea, but how about considering angle sum formulas...
ie what is
cos(n)
cos(2n)
cos(3n)
in terms of only n?

3. Aug 7, 2011

### tiny-tim

try multiplying by cos(1) …

S*cos(1) = ∑ π cos(n)cos(1)/5n = … ?