I can prove a conditionally convergent series can be made to converge to any real number ( using the idea of adding just enough positive terms to get to the number then adding just enough negative terms etc) but im not sure how to show it can be made to diverge to infinity under a suitable rearrangement.
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5Add positive terms to exceed 1. Add the first negative term. Add positive terms to exceed 2. Add the second negative term. ... – David Mitra Dec 31 '16 at 19:28
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First show that for a series that converges conditionally, both its non-positive and non-negative parts diverge. – Mark Viola Dec 31 '16 at 19:40