Question: Compute $\lim_{n\to\infty}\dfrac{1}{n}\log\left(\dfrac{n!}{n^n}\right)$.
I am supposed to "Manipulate the limit to look like a Riemann sum." I've tried to split up $\log(\frac{n!}{n^n})$ into $\log(\frac 1n)+\log(\frac 2n)...\log(\frac nn)$ but I don't know where to go from here. Any help is greatly appreciated.