MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Let ∑n=1∞an be an absolutely convergent series with sum S. Which of the following statements must be true?
(a) Any rearrangement or regrouping of the terms also converges and has sum S.
(b) Any rearrangement of the terms also converges, but the series may sum to a value different from S.
(c) The series ∑n=1∞∣an∣ converges to ∣S∣.
(d) All but finitely many terms of the series are positive.