Limit of the function with factorial and exponential Evaluate the limit
$$\large{\lim_{n\to \infty} {e^n n!\over n^n}}$$
Does the limit have a defined value?
If yes then please provide me a solution to it.

Hint
When you have problems involving factorials, Stirling approximation is very useful. A simple form is $$n! \simeq  \sqrt{2\pi n}\Big(\frac{n}{e}\Big)^n$$
I am sure that you can take from here.
