Chapter 11.4, Problem 59E

To determine

Whether the statement “Suppose that ${\displaystyle \sum a_n}$ and ${\displaystyle \sum b_n}$ are series with positive terms. If ${\displaystyle \sum a_n}$ is convergent and $b_n\ge a_n$ for all n, then ${\displaystyle \sum b_n}$ is also divergent” is true or false; explain if it is true, or give an example if it is false.