Test the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^n{7}^n}{n!}$ for convergence using the Ratio Test.

Begin by simplifying the ratio of successive terms as much as possible.

$$

$|\frac{a_{n+1}}{a_n}|=$

Then evaluate the limit of the ratio.

$\underset{n}{lim}|\frac{a_{n+1}}{a_n}|=$

$$

Based on this, the series $$