Which of the following statements correctly defines an "absolutely convergent" series?
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Which of the following statements correctly defines an "absolutely convergent" series?
(a) A series ∑an is absolutely convergent only when the Ratio Test applied to ∣an∣ yields a limit L<1.
(b) A series ∑an is absolutely convergent whenever n→∞lim∣an∣=0.
(c) A series ∑an is absolutely convergent when the series of absolute values ∑∣an∣ converges.
(d) A series ∑an is absolutely convergent when it converges and its terms alternate in sign.