Mathematics

Mathematics

Problem

Which of the following statements correctly defines an "absolutely convergent" series? a) A series ∑an\sum a_n is absolutely convergent only when the Ratio Test applied to ∣an∣|a_n| yields a limit L<1L<1. b) A series ∑an\sum a_n is absolutely convergent whenever lim⁡n→∞∣an∣=0\displaystyle\lim_{n\to\infty}|a_n|=0. c) A series ∑an\sum a_n is absolutely convergent when the series of absolute values ∑∣an∣\sum |a_n| converges. d) A series ∑an\sum a_n is absolutely convergent when it converges and its terms alternate in sign.

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