Geometric Series

A geometric series is the sum of an infinite number of terms that have a constant ration between each successive term.
\begin{align}
s & = a + ax + ax^2 + ax^3 + \cdots \\
& = \sum_{k=0}^\infty ax^k = \sum_{k=1}^\infty ax^{k-1} \\
& = \frac{a}{1-k}, \quad \text{for }|k| < 1
\end{align}
=== Proof ===
add proof