The alternating harmonic series converges but is not absolutely convergent

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The alternating harmonic series ∑n=1∞(−1)n+1n\sum_{n=1}^{\infty}\dfrac{(-1)^{n+1}}{n} converges but is not absolutely convergent. Describe what can happen to its sum if its terms are rearranged arbitrarily.

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