Determine whether this series is a convergent or divergent.

Question

Determine whether this series is a convergent or divergent.

∞

∑ [(n + 1)!]2 / ((2n + 2)!)

n=1

please explain with steps 😊

Answer 1

This series converges by the ratio test.

The ratio of 2 successive terms is [(n+2)]²/[(2n+1)(2n+3)] and the limit of this ratio is 1/4.