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BALKAN-SL 2016 A4

The positive real numbers a,b,ca, b, c satisfy the equality a+b+c=1a+b+c=1. For every natural number nn find the minimal possible value of the expression

E=a−n+b1−a+b−n+c1−b+c−n+a1−cE=\frac{a^{-n}+b}{1-a}+\frac{b^{-n}+c}{1-b}+\frac{c^{-n}+a}{1-c}

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3^{n+2}+3}{2}

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