Mathematics

Mathematics

Problem

The alternating harmonic series ∑n=1∞(−1)n+1n\displaystyle \sum_{n=1}^{\infty} \dfrac{(-1)^{n+1}}{n} converges to ln⁡2\ln 2. Which of the following is most accurate regarding its rearrangements? a) Every rearrangement converges and must still sum to ln⁡2\ln 2. 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 00 and ln⁡2\ln 2.

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