## Calculus: Early Transcendentals 8th Edition

It is not necessary that the series $\Sigma(a_{n} +b_{n})$ will be divergent.
Consider $\Sigma^{\infty}_{n=1} a_{n} = \Sigma^{\infty}_{n=1}1$ and $\Sigma^{\infty}_{n=1}b_{n} = \Sigma^{\infty}_{n=1} -1$ They are both divergent series. However, $\Sigma^{\infty}_{n=1}(a_{n} +b_{n}) = \Sigma^{\infty}_{n=1}(1+(-1)) = \Sigma^{\infty}_{n=1}0 =0$ is a convergent series. It is not necessary that the series $\Sigma(a_{n} +b_{n})$ will be divergent.