Reciprocals

Stage: 5 Challenge Level:

Prove that for any positive numbers $x_1$, $x_2$,..., $x_n$

${(x_1 + x_2 + ... + x_n)(\frac{1}{ x_1} + {1\over x_2} + ... + {1\over x_n}) \geq n^2 }$.

Published March 2002.

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