Chapter 8.4, Problem 62E

To determine

To prove: If the series ${\displaystyle \sum a_k}$ converges to A and ${\displaystyle \sum b_k}$ converges to B, then ${\displaystyle \sum _{k=1}^{\infty }\left(a_k\pm b_k\right)}=A+B$”using in the proof property 1 of Theorem 8.13.