Chapter 6.1, Problem 5E

In the following exercises, state whether each statement is true, or give an example to show that Ii is false.

5. Suppose that ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{a}_n{(x-3)}^n}$ converges at x = 6. At which of the following points must the series also converge? Use the fact that if ${\displaystyle \sum a_n{(x-c)}^n}$ conveiges at x. then ii converges at any point closer to c than x.

a. $x\text{ = 1}$

b. $x\text{ = 2}$

c. x = 3

d. x = 0

e. x =5.99 f. x = 0.000001