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December 12th, 2012, 07:49 AM  #1 
Newbie Joined: Dec 2012 Posts: 1 Thanks: 0  Can you prove this inequality?
Hi guys, I was wondering if someone can help me to solve this inequality, which is as follows: Given nonnegative numbers such that and for all , show that following holds: . I tried to solve this with AMHM 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! 
December 12th, 2012, 09:56 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  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 reuse earlier cases. 
December 19th, 2012, 07:33 PM  #3 
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Can you prove this inequality? 
December 25th, 2012, 11:51 PM  #4  
Member Joined: Jun 2012 From: Uzbekistan Posts: 59 Thanks: 0  Re: Can you prove this inequality? Quote:
 
December 26th, 2012, 12:01 AM  #5  
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Can you prove this inequality? Quote:
 

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