ThmDex – An index of mathematical definitions, results, and conjectures.
F9478
Formulation 0
Let $x_1, \dots, x_N \in (0, \infty)$ each be a D993: Real number such that
(i) $A$ is a D2454: Real arithmetic mean for $x_1, \dots, x_N$
(ii) $H$ is a D3306: Real harmonic mean for $\frac{1}{x_1}, \ldots, \frac{1}{x_N}$
Then \begin{equation} H A = 1 \end{equation}