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absolute convergence vs. conditional convergence


noun
  1. the property of an infinite series in which the series formed by replacing each term in the original series with its absolute value converges.
  2. the property of a sequence of functions in which the series whose terms are the successive differences of the elements of the sequence exhibits absolute convergence.
  3. the property of an improper integral in which the integral formed by replacing the integrand by its absolute value converges.

noun
  1. the property of an infinite series that converges while the series formed by replacing each term in the given series with its absolute value diverges; the property of an infinite series that converges when the order of the terms is altered.

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