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Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 +...

Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 + x2 + · · · + xn = 1. Prove that √ x1 + √ x2 + · · · + √ xn /√ n − 1 ≤ x1/ √ 1 − x1 + x2/ √ 1 − x2 + · · · + xn/ √ 1 − xn

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