$\sum_{n=0}^{\infty} \frac{(-1)^n x^n}{2^{n+1}}$ with $R = 2$

$\sum_{n=0}^{\infty} \frac{(-1)^n 2^n}{x^n}$ with $R = 1$

$\sum_{n=0}^{\infty} \frac{x^n}{2^n}$ with $R = 2$

$\sum_{n=0}^{\infty} (-1)^n 2^n x^n$ with $R = \frac{1}{2}$