A Serious Series

Given the fraction \(\dfrac{ax}{a-x}\), convert it into an infinite series.

The answer is: \(\displaystyle \sum_{k=0}^{\infty} \dfrac{x^{k+1}}{a^k} = x + \dfrac{x^2}{a} + \dfrac{x^3}{a^2}+\dfrac{x^4}{a^3} + \cdots\)