nice n-variable inequality

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Corei13
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nice n-variable inequality

Unread post by Corei13 » Tue Dec 21, 2010 11:16 pm

Prove that, for $a_1, a_2, \cdots a_n > 0$

\[ \left(\frac{s+a_{1}}{s-a_{1}}\right) \left(\frac{s+a_{2}}{s-a_{1}}\right) \cdots \left(\frac{s+a_{n}}{s-a_{n}} \right)\ge \left(\frac{n+1}{n-1}\right)^{n} \]

where $s=a_1+a_2+ \cdots a_n$
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