CWMO 2001 Problem 1

The sequence $\{x_n\}$ satisfies $x_1 = \frac {1}{2}, x_{n + 1} = x_n + \frac {x_n^2}{n^2}$ . Prove that $x_{2001} < 1001$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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