\begin{align*} A \amp = 2 + 4x + 10x^2 +28x^3 + 82x^4 + \cdots\\ \underline{-\qquad xA} \amp \underline{\,\,= 0 + 2x + 4x^2 + 10x^3 + 28 x^4 + 82x^5 + \cdots}\\ (1-x)A \amp = 2 + 2x + 6x^2 + 18x^3 + 54x^4 + \cdots \end{align*}