Series Matrix

Algebra Level 3

$\large {\begin{bmatrix} 2 & 1 \\ -4 & -2 \end{bmatrix}}$

Denote the matrix above as $A$ . Find the value of series below?

$I + 2A + 3A^2 + 4A^3 + \ldots$

\begin{bmatrix} 4 & 1 \\ -4 & -3 \end{bmatrix}

\begin{bmatrix} 4 & -3 \\ -8 & 5 \end{bmatrix}

\begin{bmatrix} 5 & 2 \\ -8 & -3 \end{bmatrix}

\begin{bmatrix} 5 & 3 \\ -4 & -8 \end{bmatrix}