Let $x : \mathbb{N} \to \mathbb{R}$ ne a D4685: Real sequence.
Then
| (1) | \begin{equation} \sum_{n = 0}^{\infty} x_n \in \mathbb{R} \quad \implies \quad \lim_{n \to \infty} x_n = 0 \end{equation} |
| (2) | \begin{equation} \lim_{n \to \infty} \frac{1}{n} = 0, \quad \text{ but } \quad \sum_{n = 0}^{\infty} \frac{1}{n} = \infty \end{equation} |