Chapter 8.2, Problem 62E

To determine

To prove: The series is divergent.

Answer to Problem 62E

  ${\displaystyle \sum \left(a_n+b_n\right)}$ is a divergent series.

Explanation of Solution

Given information:

  ${\displaystyle \sum a_n}$is divergent.

  ${\displaystyle \sum b_n}$ is divergent

Explain:

We know that, a series is said to be divergent series when the summation of the series gives a infinite value.

  $\begin{array}{l}\therefore {\displaystyle \sum a_n}=\infty \left[\because divergent\right]\\ and{\displaystyle \sum b_n}=\infty \left[\because divergent\right]\end{array}$

When two infinite value will be added, the resultant will be infinite.

  $\therefore {\displaystyle \sum \left(a_n+b_n\right)}=\infty$

Hence, ${\displaystyle \sum \left(a_n+b_n\right)}$ is a divergent series.