Let be a conditionally convergent series

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

Problem

Let ∑n=1∞an\sum_{n=1}^{\infty} a_n be a conditionally convergent series. Form a new series by listing all positive terms of {an}\{a_n\} first, in their original order, followed by all negative terms, also in their original order. Determine whether this rearranged series converges or diverges, and give a brief reason for your conclusion.

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