# Math Help - Another limit question...

1. ## Another limit question...

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

Here is my work:
$\lim\frac{2^n(1+(-1))}{2^{n*ln(3)}}$
since ln(3)>1 it goes to positive infinity but thatprobably wasn´t a brilliant thought...any ideas what went wrong here?

2. Originally Posted by Henryt999
$\lim_{n\rightarrow\infty}\frac{2^n+(-2)^n}{3^n}$

Here is my work:
$\lim\frac{2^n(1+(-1))}{2^{n*ln(3)}}$
since ln(3)>1 it goes to positive infinity but thatprobably wasn´t a brilliant thought...any ideas what went wrong here?

$\color{blue}\lim_{n\rightarrow\infty}\frac{2^n+(-2)^n}{3^n}=\lim_{n\to\infty} (\frac{2}{3})^n+\lim_{n\to\infty}(\frac{-2}{3})^n$

3. $\frac{2^n+(-2)^n}{3^n}=\left(\frac{2}{3}\right)^n+\left(\frac{-2}{3}\right)^n$