Answer
converges to $0$
Work Step by Step
As we know that when $x \gt 0$ so, $\lim\limits_{n \to \infty} \sqrt[n] {n}=1$ and $\lim\limits_{n \to \infty} x^{1/n}=1$ and $\lim\limits_{n \to \infty} \dfrac{x^n}{n!}=0$
Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \dfrac{(-4)^n}{n!}$
This implies that $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \dfrac{(-4)^{(n)}}{n!}=0$
Thus, $\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} converges to $0$.
