I need to determine the convergence of the following equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum_{n=0}^\infty \frac{2^n}{3^n+5}[/tex]

It's not necessary to be formal, but I would like an explination of how it's done. My belief is that it would converge to zero because although the limit is infinity over infinity, the [tex]3^n[/tex] trumps the [tex]2^n[/tex] . I tried L'Hopital's rule, however you just end up with [tex]\frac{\ln(2) * 2^n}{\ln(3) * 3^n}[/tex] over and over. I have not tried the integral technique but I don't believe that would work. Any suggestions? The sequence is geometric I think.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Determining Convergence/Divergence

**Physics Forums | Science Articles, Homework Help, Discussion**