GM-HM Inequality

Theorem
Let $x_1, x_2, \ldots, x_n \in \R_{> 0}$ be strictly positive real numbers.

Let $G_n$ be the geometric mean of $x_1, x_2, \ldots, x_n$.

Let $H_n$ be the harmonic mean of $x_1, x_2, \ldots, x_n$.

Then:
 * $G_n \ge H_n$

Also see

 * AM-HM Inequality
 * Cauchy's Mean Theorem