\begin{definition}[Definition:Harmonic Mean]
Let $x_1, x_2, \ldots, x_n \in \R$ be real numbers which are all positive.
The '''harmonic mean''' of $x_1, x_2, \ldots, x_n$ is defined as:
:$\ds H_n := \paren {\frac 1 n \paren {\sum_{k \mathop = 1}^n \frac 1 {x_k} } }^{-1}$
That is, to find the '''harmonic mean''' of a set of $n$ numbers, take the reciprocal of the arithmetic mean of their reciprocals.
\end{definition}