Limit with factorial (Stolz & Stirling) We have this limit:
$\lim\limits_{n \to \infty} (\ln(n!))/n \to \infty$
I know that it should be answered with Stolz or Stirling, but I don't know how.

Stirling's approximation tells us that the following is true:
$$ln(n!) = n \cdot ln(n) - n + O\left(ln(n)\right)$$
If we divide this by $n$, we have:
$$\frac{ln(n!)}{n} = ln(n) - 1 + O\left(\frac{ln(n)}{n}\right)$$
As $n \rightarrow \infty, \frac{ln(n!)}{n} \rightarrow \infty$.
