What's the radius of convergence of $\sum_{k=1}^{\infty}{\frac{(x-3)^k}{k\cdot 2^k}}$?

Question

What's the radius of convergence of $\sum_{k=1}^{\infty}{\frac{(x-3)^k}{k\cdot 2^k}}$?

I figured that the series converges for $1<x<5$. Does that mean that the radius of convergence is $r=5-1=4$?

Answer 1

As a power series around $3$ its radius of convergence is $2$ because it converges for $|x-3|<2$ and diverges for $|x-3| >2$.