Moderate# Limit Comparison and Integral Tests

SVCALC-WIG2KK

Does the following series converge or diverge?

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

*Hint: One way to decide this is to use Stirling's approximation for $n!$, which says that:*

$$\lim_{n\to\infty}\frac{n!}{n^n e^{-n}\sqrt{2\pi n}}=1$$