Mathematics

Mathematics

Problem

Let ∑n=1∞an\sum_{n=1}^{\infty} a_n be an absolutely convergent series with sum SS. Which of the following statements must be true? a) Any rearrangement or regrouping of the terms also converges and has sum SS. b) Any rearrangement of the terms also converges, but the series may sum to a value different from SS. c) The series ∑n=1∞∣an∣\sum_{n=1}^{\infty}|a_n| converges to ∣S∣|S|. d) All but finitely many terms of the series are positive.

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