Hello

Problem:

For which positive integer k is the following series convergent?

$\displaystyle \sum_{n=1}^{\infty} \frac{(n!)^2}{(kn)!}$

The Ratio Test seems a good choice.

After applying the Ratio Test, I will face the following limit:

$\displaystyle \lim_{n\to\infty} \frac{(n+1)^2(kn)!}{(kn+k)!}$

Then ?