Use the Ratio Test to Determine If the Series Converges $2+2+\frac{4}{3}+\frac{2}{3}+\ldots+\frac{2^{n}}{n !}+\ldots$

Short Answer

Use the ratio test to determine if the series converges of diverges:
$2+2+\frac{4}{3}+\frac{2}{3}+\ldots+\frac{2^{n}}{n !}+\ldots$