Homework Help: 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?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook