Difference between revisions of "2001 IMO Shortlist Problems/A2"
m (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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Revision as of 18:06, 20 August 2008
Problem
Let 
be an arbitrary infinite sequence of positive numbers. Show that the inequality ![$1 + a_n > a_{n - 1} \sqrt [n]{2}$](http://latex.artofproblemsolving.com/f/1/4/f14d7abe8d506e858d58a3edc4e28d7e47619a24.png)
holds for infinitely many positive integers 
.
Solution
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