Answer
Converges to $4$
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \sqrt [n] {4^n n}$
Since, $\lim\limits_{n \to \infty} \sqrt[n] {n}=1$ and $\lim\limits_{n \to \infty} x^{1/n}=1$ when $x \gt 0$
So, $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \sqrt [m] {4^n n}=4 \lim\limits_{n \to \infty}\sqrt [n] {n} =(4)(1)=4$
Hence, $\lim\limits_{n \to \infty} a_n=4$ and {$a_n$} is Convergent and converges to $4$
