Let $x : \mathbb{N} \to \mathbb{R}$ be a D4685: Real sequence.
Then
| (1) | \begin{equation} N \in \{ 1, 2, 3, \ldots \} \quad \implies \quad \sum_{n = 0}^N (x_{n - 1} - x_n) = x_N - x_0 \end{equation} |
| (2) | \begin{equation} \lim_{n \to \infty} x_n = 0 \quad \implies \quad \sum_{n = 0}^{\infty} (x_{n + 1} - x_n) = - x_0 \end{equation} |