Chapter 11.3, Problem 45E

In Exercises 45–48, determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

45. If ${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}(a_n+b_n)}$ converges, then both ${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{a}_n}$ and ${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{b}_n}$ must converge.