Chapter 9.8, Problem 58ES

Suppose that the power series ${\displaystyle \sum c_k{(x-x_0)}^k}$ has a finite radius of convergence $R_1$ and the power series ${\displaystyle \sum d_k{(x-x_0)}^k}$ has a finite radius of convergence $R_2.$ What can you say about the radius of convergence of ${\displaystyle \sum (c_k}+d_k){(x-x_0)}^k?$ Explain your reasoning.