CPM Homework Help : CALC Problem 10-41

Find two different series $S =\displaystyle \sum _ { n = 1 } ^ { \infty } a _ { n }$ and $T =\displaystyle \sum _ { n = 1 } ^ { \infty } b _ { n }$ ( $b _ { n } \neq 0$ ) such that $S$ and $T$ both diverge yet the series $U =\displaystyle \sum _ { n = 1 } ^ { \infty } ( a _ { n } - b _ { n } )$ converges.

Hint:

Any series of the following form diverge. Use series of this form to determine your answer.
$\displaystyle \sum_{n=1}^{\infty}\frac{a}{bn+c}$