Answer
The sequence $a_n$ converges to $0$.
Work Step by Step
We have
$$\lim_{n\to \infty}a_n=\lim_{n\to \infty}\frac{n}{2^n}=\frac{\infty}{\infty}
.$$
By L'Hopital's rule, we have
$$ \lim_{n\to \infty}\frac{n}{2^n}= \lim_{n\to \infty}\frac{1}{2^n\ln 2}=0
.$$
Hence, by Theorem 1, the sequence $a_n$ converges to $0$.
