Let $x_1, \dots, x_N \in (0, \infty)$ each be a D5407: Positive real number.
Then
| (1) | \begin{equation} \frac{1}{\frac{1}{N} \sum_{n = 1}^N \frac{1}{x_n}} \leq \left( \prod_{n = 1}^N x_n \right)^{\frac{1}{N}} \end{equation} |
| (2) | \begin{equation} \frac{1}{\frac{1}{N} \sum_{n = 1}^N \frac{1}{x_n}} = \left( \prod_{n = 1}^N x_n \right)^{\frac{1}{N}} \quad \iff \quad \frac{1}{x_1} = \frac{1}{x_n} = \cdots = \frac{1}{x_N} \end{equation} |