Answer
Converges
Work Step by Step
In order to solve the given series we will take the help of Ratio Test. This test states that when the limit $L \lt 1$ , the series converges and for $L \gt 1$, the series diverges.
Here, $a_n=\dfrac{2^n}{n!}$
$L=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{2^{n+1}}{(n+1)!}}{\dfrac{2^n}{n!}}|$
Thus, we have $L=\lim\limits_{n \to \infty}|\dfrac{2}{n+1}|=\lim\limits_{n \to \infty}|\dfrac{2/n}{1+1/n}|$
so, $L=0 \lt 1$
Hence, the series Converges by the ratio test.