Determine if $$\sum^{\infty}_{n=0} \dfrac{1+2^n}{3^n}$$ converges or diverges.
The tests I know so far are: by defintion, geometric, divergence, integral
Unfortunately none of them worked for me. Definition doesn't, this is not a geometric sum, divergence does not apply, and the integral is too complicated in this case.
What can I do?