Arithmetic_Mean_is_Never_Less_than_Harmonic_Mean

Let $x_1, x_2, \ldots, x_n \in \R_{> 0}$ be strictly positive real numbers. Let $A_n$ be the arithmetic 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 $A_n \ge H_n$.