Determine whether the series

$($a$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{(n+1)!}{e^{n^2}}$

$($b$){\displaystyle \underset{n=1}{\overset{}{}}}(\frac{-2n}{n+1}{)}^{5n}.$

are convergent or divergent.