Sum of Infinite Geometric Sequence/Corollary 2

Corollary to Sum of Infinite Geometric Sequence
Let $S$ be a standard number field, that is $\Q$, $\R$ or $\C$.

Let $z \in S$.

Let $\size z < 1$, where $\size z$ denotes:
 * the absolute value of $z$, for real and rational $z$
 * the complex modulus of $z$ for complex $z$.

Then:
 * $\ds \sum_{n \mathop = 0}^\infty a z^n = \frac a {1 - z}$