N'th power inequality

For discussing Olympiad Level Algebra (and Inequality) problems
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zadid xcalibured
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N'th power inequality

Unread post by zadid xcalibured » Sat Apr 06, 2013 12:52 am

All $a_{i}$ are positive real numbers.Prove that,
\[\sum_{cyclic} \frac{1}{a_{i}^{n}+a_{i+1}^{n}+......................+a_{i+n-2}^{n}+a_{1}a_{2}.....a_{n}} \leq \frac{1}{a_{1}a_{2}..........a_{n}}\]

User avatar
zadid xcalibured
Posts: 217
Joined: Thu Oct 27, 2011 11:04 am
Location: mymensingh

Re: N'th power inequality

Unread post by zadid xcalibured » Sat Apr 06, 2013 2:04 am

This is not some problem i came across.It is a generalization of a problem by Mehfuz Zohir Shishir.I posted this on behalf of him.He forgot his forum password.

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