\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*}

\begin{gather*} \sum_{k=0}^{\infty} {(x-b)^k} = \frac{1}{1-(x-b)}, |x-b| \lt 1 \end{gather*}