Chapter 9.8, Problem 2QCE

Since $\underset{k\to +\infty }{\lim }\left|\frac{2^{k+1}{x}^{k+1}}{2^k{x}^k}\right|=2\left|x\right|$ the radius of convergence for the infinite series ${\displaystyle {\sum }_{k=0}^{\infty }{2}^k}{x}^k\text{is\_\_\_\_\_\_}\text{.}$