ThmDex – An index of mathematical definitions, results, and conjectures.
F11612
Formulation 0
Let $q \in [0, 1)$ be an D4767: Unsigned real number.
Let $N \in 1, 2, 3 \ldots$ be a D5094: Positive integer.
Then \begin{equation} \sum_{n = 0}^N q^n = \frac{1 - q^{N + 1}}{1 - q} = \frac{q^{N + 1} - 1}{q - 1} \end{equation}