olymmath

NZ-NZMO 2019 Problem 8

    Suppose that x1,x2,x3,…xnx_{1},x_{2},x_{3},\ldots x_{n} are real numbers between 0 and 1 with sum ss . Prove that

    ∑i=1nxis+1−xi+∏i=1n(1−xi)≤1.\sum_{i = 1}^{n}{\frac{x_{i}}{s + 1 - x_{i}}} + \prod_{i = 1}^{n}(1 - x_{i})\leq 1.

    Dataset text NuminaMath olympiads. Quoted with source.

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