Algebra Level 4

Let $A = \left( \begin{matrix} 4 & 2 \\ 2 & 2 \end{matrix} \right)$ Evaluate $\displaystyle \sum_{n = 1}^{\infty} \det (4(A^{-1})^{n})$ The above expression has a closed form. Give your answer to 3 decimal places.

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