Chapter 11, Problem 22TFQ

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

If ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{a}_n}=A$ and ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{b}_n}=B$, then ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{a}_n{b}_n}=AB$.