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1985 IMO Problems/Problem 6

Revision as of 10:54, 25 July 2012 by DAFR (talk | contribs) (Created page with "For every real number <math>x_1</math>, construct the sequence <math>x_1,x_2,\ldots</math> by setting <math>x_{n+1}=x_n \left(x_n + \frac{1}{n}\right)</math> for each <math>n \ge...")
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For every real number $x_1$, construct the sequence $x_1,x_2,\ldots$ by setting $x_{n+1}=x_n \left(x_n + \frac{1}{n}\right)$ for each $n \geq 1$. Prove that there exists exactly one value of $x_1$ for which $0<x_n<x_{n+1}<1$ for every $n$.

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