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IMO ShortList 1998, algebra problem 2

Source: IMO ShortList 1998, algebra problem 2

October 22, 2004
inequalitiesfunctionalgebran-variable inequalityIMO Shortlist

Problem Statement

Let r1,r2,…,rnr_{1},r_{2},\ldots ,r_{n} be real numbers greater than or equal to 1. Prove that 1r1+1+1r2+1+⋯+1rn+1≥nr1r2⋯rnn+1. \frac{1}{r_{1} + 1} + \frac{1}{r_{2} + 1} + \cdots +\frac{1}{r_{n}+1} \geq \frac{n}{ \sqrt[n]{r_{1}r_{2} \cdots r_{n}}+1}.
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