Given any series , we define a series whose terms are all
Chapter 11, Problem 11.351(choose chapter or problem)
Given any series , we define a series whose terms are all the positive terms of and a series whose terms are all the negative terms of . To be specific, we let Notice that if , then and , whereas if , then and . (a) If is absolutely convergent, show that both of the series and are convergent. (b) If is conditionally convergent, show that both of the series and are divergent.
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