# Determine if series converges

1. Mar 26, 2013

### whatlifeforme

1. The problem statement, all variables and given/known data
Determine if series converges or diverges.

2. Relevant equations
$\displaystyle \sum^{∞}_{n=0} \frac{cos n* \pi}{5^n}$

3. The attempt at a solution
I have tried using the nth term test but not sure how to take the limit of cosine.

2. Mar 26, 2013

### Curious3141

Why don't you try working out the value of that cosine term for the first few values of n and see what you get?

Another hint: absolute convergence.

3. Mar 26, 2013

### HallsofIvy

Staff Emeritus
First, $cos(n\pi)$ is just $(-1)^n$ so this is $\frac{(-1)^n}{5^n}$ and the ratio test works nicely.

4. Mar 26, 2013

### Zondrina

What is $\sum |a_n|$, can it be bounded in some way?

Then perhaps another test will clean the rest up for you.