Chapter 11.5, Problem 4CQ

To determine

To explain: About the convergence or divergence of ${\displaystyle \sum _{n=0}^{\infty }{a}_n}{5}^n$ and ${\displaystyle \sum _{n=0}^{\infty }{a}_n}{\left(\frac{1}{2}\right)}^n$ if ${\displaystyle \sum _{n=0}^{\infty }{a}_n}{\left(x-2\right)}^n$ diverges for $x=0$.