I'm supposed to study the convergence of this series and consider separately the cases of $a > 1$ and $a \leq 1$ :

Let $a \geq 0$. 

$$\sum\_{n \geq1} \frac{1}{(a^n+n)}$$

I've tried using the integral test and the simplest divergence test. I've noticed it's a geometric series when $a = 2$ but I'm having trouble getting anything rigorous. Any help is appreciated.