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cyclic sum 1 / (a(b+1)) + ... >= 3 / (1+abc)

Source: Balkan MO 2006, Problem 1; Crux 1998, proposed by Mohammed Aassila; Kömal; ...

August 17, 2003
inequalitiesrearrangement inequalityinequalities theoremsinequalities proposed

Problem Statement

Let a a, b b, c c be positive real numbers. Prove the inequality 1a(b+1)+1b(c+1)+1c(a+1)≥31+abc. \frac{1}{a\left(b+1\right)}+\frac{1}{b\left(c+1\right)}+\frac{1}{c\left(a+1\right)}\geq \frac{3}{1+abc}.
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