Find radius of convergence for
$$\sum_{n=1}^{\infty} \frac{(x-1)^{n-3} + (x-1)^{n-1}}{4^n + 2^{2n-1}}$$
What I did:
$$\sum_{n=1}^{\infty} \frac{(x-1)^n ((x-1)^{-3} + (x-1)^{-1})}{2^{2n}(1+2^{-1})}$$
$$= \sum_{n=1}^{\infty} \frac{2}{3} ((x-1)^{-3} + (x-1)^{-1}) (\frac{x-1}{4})^n$$
$$L = |\lim_{x \to \infty} \frac{x-1}{4}| = \infty$$
$$R = L^{-1} = 0$$
But correct answer is 4