Chapter 11.1, Problem 2TFR

To determine

To find:

Whether if ${\displaystyle \sum _{n=0}^{\infty }{a}_n{x}^n}$ and ${\displaystyle \sum _{n=0}^{\infty }{b}_n{x}^n}$ both converge at $x=x_1$, then so does ${\displaystyle \sum _{n=0}^{\infty }\left(a_n+b_n\right)x^n}$ is true or false.