Use the Ratio Test to determine the convergence or divergence of the series. $($If you nee

$,{\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^{n+1}n!}{1*4*7\text{c}\text{d}\text{o}\text{t}\text{s}(3n+1)}$

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