Q:

Question about the Geometric Sequence Theorem

I am reading my professor's notes, and there is something that I'm not understanding about this.  The Geometric Sequence Theorem states that if $r$ is a real number such that $|r| < 1$, then $\lim_{n\to\infty} r^n = 0$. I understand that well enough, but then she gives us an example that asks whether $(2^n/3^{n+1})$ is convergent.  
She ends up writing:
\begin{align*}
\lim_{n \to infty} (a_n)
&= \lim_{n\to \infty}\frac{2^n}{3^{n+1}} \\
&= \frac 1 3 \lim_{n\to \infty}\frac{2^n}{3^n}
\end{align*}
and I'm wondering how in the WORLD she took a $1/3$ out of there. 
Also, is the geometry sequence theorem basically stating that if $r$ is a fraction, then $r^n = 0$? 

A:

Hint --I don't have enough points for a comment:
$3^{n+1}=3(3^n)$ , so that $\frac {2^n}{3^{n+1}}$ =$\frac {2^n}{3.3^n}=....$
And, be careful; if r is a fraction with ratio between -1 and 1 (non-inclusive), then
$r^n\rightarrow 0$ as $n \rightarrow \infty$

