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2009 USAMO Problems/Problem 4

Revision as of 09:39, 12 June 2009 by JBrere (talk | contribs) (New page: == Problem == For <math>n \ge 2</math> let <math>a_1</math>, <math>a_2</math>, ..., <math>a_n</math> be positive real numbers such that <cmath> (a_1+a_2+ ... +a_n)\big( {1 \over a_1} + {1...)
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Problem

For $n \ge 2$ let $a_1$, $a_2$, ..., $a_n$ be positive real numbers such that \[(a_1+a_2+ ... +a_n)\big( {1 \over a_1} + {1 \over a_2} + ... +{1 \over a_n} \big) \le \big(n+ {1 \over 2} \big) ^2\] Prove that max $(a_1, a_2, ... ,a_n)$ $\le$ 4 min $(a_1, a_2, ... , a_n)$.

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