Let $p \in [0, \infty)$ be an D4767: Unsigned real number.
Then
| (1) | \begin{equation} \sum_{n = 1}^{\infty} \frac{1}{n^p} = \infty \quad \iff \quad p \in [0, 1] \end{equation} |
| (2) | \begin{equation} \sum_{n = 1}^{\infty} \frac{1}{n^p} \in [0, \infty) \quad \iff \quad p \in (1, \infty) \end{equation} |