Chapter 11.4, Problem 2PQ

To determine

Which of the following statement is equivalent to Theorem 1?

a. If ${\displaystyle \sum _{n=0}^{\infty }\left|a_n\right|}$ diverges, then ${\displaystyle \sum _{n=0}^{\infty }{a}_n}$ also diverges.

b. If ${\displaystyle \sum _{n=0}^{\infty }{a}_n}$ diverges, then ${\displaystyle \sum _{n=0}^{\infty }\left|a_n\right|}$ also diverges.

c. If ${\displaystyle \sum _{n=0}^{\infty }{a}_n}$ converges, then ${\displaystyle \sum _{n=0}^{\infty }\left|a_n\right|}$ also converges.