RO-TST 2010 Problem 6

Given a positive integer number $n$ , determine the minimum of $$\max \left\{\dfrac{x_1}{1 + x_1}, \dfrac{x_2}{1 + x_1 + x_2}, \cdots, \dfrac{x_n}{1 + x_1 + x_2 + \cdots + x_n}\right\},$$ as $x_1, x_2, \ldots, x_n$ run through all non-negative real numbers which add up to $1$ .

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