Alternative Definition
Unconditional convergence is often defined in an equivalent way: A series is unconditionally convergent if for every sequence, with, the series
converges.
Every absolutely convergent series is unconditionally convergent, but the converse implication does not hold in general. When X = Rn, then, by the Riemann series theorem, the series is unconditionally convergent if and only if it is absolutely convergent.
Read more about this topic: Unconditional Convergence
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