Let $z \in \mathbb{C}$ be a D1207: Complex number.
Then
| (1) | \begin{equation} \sum_{n = 0}^{\infty} z^n \in \mathbb{C} \quad \iff \quad |z| \in [0, 1) \end{equation} |
| (2) | \begin{equation} |z| \in [0, 1) \quad \implies \quad \sum_{n = 0}^{\infty} z^n = \frac{1}{1 - z} \end{equation} |