# Prove x^n < n!

1. Sep 21, 2009

### dannysaf

proof xn < n!

2. Sep 21, 2009

### efekwulsemmay

We would be happy to help you if you at least try the problem yourself and show us what you have tried

3. Sep 21, 2009

### Office_Shredder

Staff Emeritus
Obviously not.

31>1!

Have you started trying to prove it yet? Presumably the question asks to prove that for large enough n.... what are your initial thoughts?

4. Sep 21, 2009

### Gregg

Maybe he means n^n<n! becuase there is always $$x=n!^{1\over n}$$ ?

If so, you need to construct your argument around n^n = n*n*n*n...*n (n times) and n! = n(n-1)(n-2)...3.2.1 I think.

5. Sep 21, 2009

### Staff: Mentor

Perhaps for n approaching infinity?