MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
The alternating harmonic series n=1∑∞n(−1)n+1 converges to ln2. Which of the following is most accurate regarding its rearrangements?
(a) Every rearrangement converges and must still sum to ln2.
(b) The series can be rearranged to converge to any prescribed real number.
(c) Every rearrangement diverges because the series is not absolutely convergent.
(d) A rearrangement may change the sum, but it can only produce values between 0 and ln2.