Does the Series \(\sum_{n=1}^{\infty} \frac{n+2^n}{n+3^n}\) Converge or Diverge?

[Askhwhelp]

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

 

[Office_Shredder]

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