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December 12th, 2012, 07:49 AM   #1
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Can you prove this inequality?

Hi guys,

I was wondering if someone can help me to solve this inequality, which is as follows:

Given non-negative numbers such that and for all , show that following holds: .

I tried to solve this with AM-HM inequality and few other ways, but without success. Only thing I can prove is for special case . I've checked this programmatically (in a few ways) and haven't found any counterexample, so I think it should be correct. I proposed this by myself, haven't found anywhere else on the internet.

Does anyone know solution? Or anyone can give me some suggestion?

Thanks in advance!
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December 12th, 2012, 09:56 AM   #2
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Re: Can you prove this inequality?

Hmm... the first approach that springs to mind is to alter the statement to

, for such that



for any

This way hopefully it is easier to use induction, since the last term is implicit so you can re-use earlier cases.
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December 19th, 2012, 07:33 PM   #3
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Re: Can you prove this inequality?




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December 25th, 2012, 11:51 PM   #4
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Re: Can you prove this inequality?

Quote:
Originally Posted by tahir.iman



How did you prove ?
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December 26th, 2012, 12:01 AM   #5
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Re: Can you prove this inequality?

Quote:
Originally Posted by golomorf
Quote:
Originally Posted by tahir.iman



How did you prove ?
Oh, i have mistake there, i am on it.
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