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