\begin{align*} 2 + 4x + 10x^2 + 28x^3 + \cdots \amp = (1 + 1) + (1 + 3)x + (1 + 9)x^2 + (1 + 27)x^3 + \cdots\\ \amp = 1 + x + x^2 + x^3 + \cdots + 1 + 3x + 9x^2 + 27x^3 + \cdots\\ \amp = \frac{1}{1-x} + \frac{1}{1-3x} \end{align*}
in-context