Chapter 5.5, Problem 289E

For the following exercises, indicate whether each of the following statements is true or false. If the statement is false, provide an example in which it is false.

289. If $b_n\ge 0$ is decreasing and ${\displaystyle \underset{n1}{\overset{\infty }{\sum }}\left(b_{3n-2}+b_{3n-1}-b_{3n}\right)}$ converges then ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{b}_{3n-2}}$ converges.