Ky Fan inequality

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In mathematics, the Ky Fan inequality states that if xi for i = 1, ..., n are real numbers satisfying

0 < x_i <\frac{1}{2},

then

\frac{ (\Pi_{i=1}^n x_i )^{\frac{1}{n}}}{ (\Pi_{i=1}^n (1- x_i) )^{\frac{1}{n} }} \leq \frac{ \frac{1}{n} \sum_{i=1}^n x_i }{ \frac{1}{n} \sum_{i=1}^n (1- x_i) }.
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