Prove by induction that n! > (n/3)^n
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Sorry, I made a mistake: the following doesn't help much. Originally Posted by h2osprey Prove by induction that n! > (n/3)^n n = 1: 1! = 1 > (1/3)^1 n -> n+1
Last edited by Rapha; Jan 8th 2009 at 08:08 PM.
Originally Posted by Rapha n = 1: 1! = 1 > (1/3)^1 n -> n+1 Shouldn't it be ?
Originally Posted by h2osprey Prove by induction that n! > (n/3)^n to complete your induction use the identity: and this fact that: note that the solution is actually suggesting a stronger inequality, i.e.
Here is a non-induction proof:
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