# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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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The novel's three alternating series of chapters are anchored in 1961, the year of Trujillo's assassination.
The Bears have been grooming rookie James Daniels to become a starter since Week 4, when he began alternating series with Kush, and the second-round pick from Iowa got his first start Sunday when the veteran was sidelined.

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