# Comparison Tests for Series

1. Jul 6, 2011

### waealu

1. The problem statement, all variables and given/known data
Does the following series converge or diverge (use either the Limit Comparison or the Direct Comparison Test):

$$\sum_{n=1}^{+\infty} \frac{3^{n-1}+1}{3^{n}}$$

2. Relevant equations

In a previous problem that was
$$\sum_{n=1}^{+\infty} \frac{1}{3^{n-1}+1}$$
I was able to reindex the series to make it
$$\sum_{n=0}^{+\infty} \frac{1}{3^{n}+1}$$
From there, I took 1/(3n+1)<1/3n.

Therefore, since 1/3n converges, $$\sum_{n=1}^{+\infty} a_{n}$$ also converges.

3. The attempt at a solution

However, I don't know how to solve the series that I'm currently on.

Thanks,
Erik

2. Jul 6, 2011

### Dick

(3^(n-1)+1)/3^n>1/3, isn't it?