Reciprocals

Problem | Hint | Solution | Printable page |
Stage: 5 Challenge Level: Challenge Level:1

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

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


Published March 2002.