\begin{definition}[Definition:Geometric Mean]
Let $x_1, x_2, \ldots, x_n \in \R_{>0}$ be (strictly) positive real numbers.
The '''geometric mean''' of $x_1, x_2, \ldots, x_n$ is defined as:
:$\ds G_n := \paren {\prod_{k \mathop = 1}^n x_k}^{1/n}$
That is, to find out the '''geometric mean''' of a set of $n$ numbers, multiply them together and take the $n$th root.
\end{definition}