Answer
Converges
Work Step by Step
Consider $a_n=\dfrac{2^n}{n!}$
Now, $l=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{2^{n+1}}{(n+1)!}}{\dfrac{2^n}{n!}}|$
Thus, we have $l=\lim\limits_{n \to \infty}|\dfrac{2}{n+1}|=0 \lt 1$
Hence, the series Converges absolutely by the ratio test.