$\displaystyle \lim_{n\rightarrow\infty}\frac{2^n+(-2)^n}{3^n}$

Here is my work:

$\displaystyle \lim\frac{2^n(1+(-1))}{2^{n*ln(3)}} $

since ln(3)>1 it goes to positive infinity but thatprobably wasn´t a brilliant thought...any ideas what went wrong here?