Do you remember summer '09?

Calculus Level 4

$\displaystyle \lim_{n \to \infty}\left(\dfrac{n!}{(mn)^n}\right)^{1/n}$

Let $m$ be a constant positive number. Evaluate the limit above for integer $n$ .

Clarification: $e$ denotes Euler's number, $e \approx 2.71828$ .