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        riddles >> medium >> Prove a^n>n^a
        
(Message started by: wonderful on Apr 29th, 2008, 12:14am)
Title: Prove a^n>n^a
Post by wonderful on Apr 29th, 2008, 12:14am
Given a>=2 and n>a^2,

prove a^n>n^a.

Have A Great Day!
Title: Re: Prove a^n>n^a
Post by Aryabhatta on Apr 29th, 2008, 12:42am
[hide] f(x) = x^(1/x) is increasing in (0,e] and decreasing in [e, oo) [/hide]
Title: Re: Prove a^n>n^a
Post by rmsgrey on Apr 29th, 2008, 7:15am

on 04/29/08 at 00:42:29, Aryabhatta wrote:
[hide] f(x) = x^(1/x) is increasing in (0,e] and decreasing in [e, oo) [/hide]

And
[hide]2^(1/2)=4^(1/4)[/hide]


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