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ASU 172 All Soviet Union MO 1972 min of max of ... , x_n/(1+x_1+...+x_n)

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July 3, 2019
minimummaximumalgebrainequalities

Problem Statement

Let the sum of positive numbers x1,x2,...,xnx_1, x_2, ... , x_n be 11. Let ss be the greatest of the numbers {x11+x1,x21+x1+x2,...,xn1+x1+...+xn}\left\{\frac{x_1}{1+x_1}, \frac{x_2}{1+x_1+x_2}, ..., \frac{x_n}{1+x_1+...+x_n}\right\} What is the minimal possible ss? What xix_i correspond it?
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