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2001 IMO Shortlist Problems/A2

Revision as of 17:06, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Let <math>a_0, a_1, a_2, \ldots</math> be an arbitrary infinite sequence of positive numbers. Show that the inequality <math>1 + a_n > a_{n - 1} \sqrt [n]{2}</math> holds fo...)
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Problem

Let $a_0, a_1, a_2, \ldots$ be an arbitrary infinite sequence of positive numbers. Show that the inequality $1 + a_n > a_{n - 1} \sqrt [n]{2}$ holds for infinitely many positive integers $n$.

Solution

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Resources

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