# Convergence or divergence

1. Oct 30, 2013

The sum is $$\sum_{n=1}^{\infty} \frac{n+2^n}{n+3^n}$$ Is this convergent or divergent? I tried to use the divergent test but the test fail because $a_n = (n+2^n)/(n+3^n) = 0$ as $n$ goes to infinity. Could someone point me to the right direction?

Thanks

2. Oct 30, 2013

### Office_Shredder

Staff Emeritus
What are some other tests that you know? Can you apply any of them?