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.

With Stolz:
$$ \lim_{n\to +\infty}\frac{\log(n)}{1}=+\infty\quad\Longrightarrow\quad \lim_{n\to +\infty}\frac{\sum_{k=1}^{n}\log(k)}{\sum_{k=1}^{n}1}=+\infty.$$
With Stirling:
$$ n!\geq \left(\frac{n}{e}\right)^n \sqrt{2\pi n}\quad\Longrightarrow\quad \log(n!)\geq n\log(n)-n.$$
With Hermite-Hadamard ($\log x$ is concave on $\mathbb{R}^+$):
$$ \log(n!)=\sum_{k=1}^{n}\log(k)\geq \frac{1}{n}\int_{1/2}^{n+1/2}\log(x)\,dx=\left(n+\tfrac{1}{2}\right)\log(2n+1)-(1+\log 2)n. $$
