In mathematics, a series (or sometimes also an integral) of numbers is said to converge absolutely if the sum (or integral) of the absolute value of the summand or integrand is finite. More precisely, a real or complex-valued series is said to converge absolutely if Absolute convergence is vitally important to the study of infinite series because on the one hand, it is strong enough that such series retain certain basic properties of finite sums—the most important ones being rearrangement of the terms and convergence of products of two infinite series—that are unfortunately not possessed by all convergent series. On the other hand absolute convergence is weak enough to occur very often in practice. Indeed, in some (though not all) branches of mathematics in which series are applied, the existence of convergent but not absolutely convergent series is little more than a curiosity.

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