1989 APMO Problems/Problem 1

Problem

Let $x_1$ , $x_2$ , $\cdots$ , $x_n$ be positive real numbers, and let $S = x_1 + x_2 + \cdots + x_n.$ Prove that $(1 + x_1)(1 + x_2) \cdots (1 + x_n) \leq 1 + S + \frac{S^2}{2!} + \frac{S^3}{3!} + \cdots + \frac{S^n}{n!}$

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1989 APMO Problems/Problem 1

Problem

Solution