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[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.