Is it possible to make an absolutely convergent series from two conditional convergent series? Just to be more clear, if we have an absolutely convergent series, we can rearrange the terms and possible separate the terms to make two separate new series. Would it be possible for one or both of those series to be conditionally convergent?
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You can't. A series converges absolutely, iff it's absolute-values make a [non-negative] convergent series. But a non-negative series can't converge if it has a non-converging sub-sequence.