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   Author  Topic: Prove a^n>n^a  (Read 496 times)
wonderful
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Prove a^n>n^a  
« on: Apr 29th, 2008, 12:14am »		 Quote Quote Modify Modify
Given a>=2 and n>a^2,
 
prove a^n>n^a.
 
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Aryabhatta
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Re: Prove a^n>n^a  
« Reply #1 on: Apr 29th, 2008, 12:42am »		 Quote Quote Modify Modify
f(x) = x^(1/x) is increasing in (0,e] and decreasing in [e, oo)
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rmsgrey
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Re: Prove a^n>n^a  
« Reply #2 on: Apr 29th, 2008, 7:15am »		 Quote Quote Modify Modify
on Apr 29th, 2008, 12:42am, Aryabhatta wrote:
f(x) = x^(1/x) is increasing in (0,e] and decreasing in [e, oo)

And
2^(1/2)=4^(1/4)
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