ThmDex – An index of mathematical definitions, results, and conjectures.
F9476
Formulation 0
Let $x_1, \dots, x_N \in (0, \infty)$ each be a D993: Real number such that
(i) $a \in (0, \infty)$ is a D3306: Real harmonic mean of $x_1, \dots, x_N$
Then \begin{equation} a = \frac{N}{\sum_{n = 1}^N \frac{1}{x_n}} \end{equation}