Answer
Converges
Work Step by Step
Apply the Ratio test to the Series
$\Sigma^{\infty}_{n=0} \frac{2^n}{n!}$
$\lim\limits_{n \to \infty} |\frac{\frac{2^{n+1}}{(n+1)!}}{\frac{2^n}{n!}}|$
$\lim\limits_{n \to \infty} \frac{2(n!)}{(n+1)!}$
$\lim\limits_{n \to \infty} \frac{2}{(n+1)} = 0<1$
Because the answer is less than 1, the series converges
