Proof by induction -- Inequalities
Posted on 2009-04-03
Ok I can't figure out how to inductively prove the following inequalities, I have the base case and inductive hypothesis, I just don't see how to prove this stuff. I've already turned in the assignment, I'm just curious cause they never tell us. At least there's points in it for you guys.
1.) Prove that n! > n^3 when n is large enough. (n has to be greater than or equal to 6)
2.) Prove that n! < n^n for all positive integers by induction.
I just can't seem to prove these inequalities for P(K+1). Any help would be appreciated.
-Jeff P.S. (If you solve one I'll give you half the points, unless only one is ever solved than I'll give you them all! HAHAHA)