# Alternating Series

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## alternating series

[′ȯl·tər·nād·iŋ ′sir·ēz]
(mathematics)
Any series of real numbers in which consecutive terms have opposite signs.

## Alternating Series

an infinite series whose terms are alternately positive and negative:

u1 - u2 + u3 - u4 + … + (-I)n-1un + …

for uk > 0. If the terms of an alternating series monotonically decrease (un+1 < un) and tend toward zero (lim un = 0), then the series is convergent (the Leibniz theorem). The remainder of the convergent series

rn = (-1)nun+1 + …

has the sign of its first term and is less than this term in absolute value. Some very simple examples of convergent alternating series are

References in periodicals archive ?
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Others suggest creative solutions taken by Weitz to deliver key passages in the book; for example, the film summarizes Nick's complicated childhood via a game of catch, panning back and forth between a boyhood Nick (Liam Broggy) and an alternating series of father figures.
We now develop double integral identities for S (a, b, j, k), S(a, b, j, k, m) and their alternating series companions and, moreover, recover and extend some of the results obtained by Guillera and Sondow (1) such as
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The novel's three alternating series of chapters are anchored in 1961, the year of Trujillo's assassination.
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He completed 8 of 12 passes for 119 yards and two touchdowns while alternating series with Jason Soporito.

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