Answer
$\lim\limits_{n \to \infty} a_n=0 $ and {$a_n$} is convergent
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \dfrac{ n}{2^n}$
But $\lim\limits_{n \to \infty} \dfrac{ n}{2^n}=\dfrac{\infty}{\infty}$
We need to apply L-Hospital's rule:
So, $\lim\limits_{n \to \infty} \dfrac{ n}{2^n}=\lim\limits_{n \to \infty} \dfrac{1}{2^n \ln 2}=0$
Hence, $\lim\limits_{n \to \infty} a_n=0 $ and {$a_n$} is convergent
