Given the series

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(n!{)}^3}{(7n)!}$

find the ratio $|\frac{a_{n+1}}{a_n}|.$

$($Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

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

Use the Ratio Test,to determine the correct statement.

The series diverges.

The Ratio Test is inconclusive.

The series converges.