Example 12.1.4. Playing with the base.
\begin{align*}
\sum_{k=0}^{\infty} {a^k x^k} & = \sum_{k=0}^{\infty} {(ax)^k}\\
& = \frac{1}{1-ax}, |x| \lt \frac{1}{a}
\end{align*}
or perhaps
\begin{gather*}
\sum_{k=0}^{\infty} {(x-b)^k} = \frac{1}{1-(x-b)}, |x-b| \lt 1
\end{gather*}