I need to find the limit as $\lim_{n\to\infty}\frac{n!}{n^n}$ via the Sandwich/Squeeze Theorem.
I've been stuck on this for a while as I can't say either the numerator or denominator is bound.
Edit: I'm sorry that I wasn't more explicit when I posted this, I hadn't used this site before this question. The reason why I have to use the above theorem is because it's a question set in one of university problem sheets and I've honestly been stuck on it for several weeks. My only real attempt to solve it was: $$\lim_{n \to \infty}\frac{n!}{n^n}$$ $$0\le\frac{1}{n^n}\le1$$ $$0\le\frac{n!}{n^n}\le n!$$ $$\lim_{n\to\infty}0\le\lim_{n\to\infty}\frac{n!}{n^n}\le\lim_{n\to\infty}n!$$ Which leaves the issue that $\lim_{n\to\infty}n!$ is undefined, so the middle limit isn't bound, and so I can't make the final conclusive statement. All my other attempts were just as unsuccessful as this one. I already know that the limit is zero, but because the question states that I must use the Sandwich/Squeeze theorem, I'm completely stuck.