# series

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## series,

in mathematics, indicated sum of a sequencesequence,
in mathematics, ordered set of mathematical quantities called terms. A sequence is said to be known if a formula can be given for any particular term using the preceding terms or using its position in the sequence.
of terms. A series may be finite or infinite. A finite series contains a definite number of terms whose sum can be found by various methods. An infinite series is a sum of infinitely many terms, e.g., the infinite series 1-2 + 1-4 + 1-8 + 1-16 + … . The dots mean that the remaining terms are formed according to the rule made evident by the first few terms, in this case doubling the denominator of the preceding term to form that of the next term; the nth term of this series is ( 1-2)n. Some infinite series converge to a certain value called its limit; i.e., as one adds together progressively more terms, these sums (called the partial sums of the series) form a sequence of values that progressively approach the limit. For example, the series given above converges to the value 1 because the partial sums form the sequence 1-2, 3-4, 7-8, 15-16, … . Many series, however, do not converge, i.e., have no value that their partial sums approach. Such a series is 1-2 + 1-3 + 1-4 + … , for even though the terms become very small, enough of them added together will give a value greater than any number that can be named. A series that does not converge is said to diverge; various tests exist for determining whether or not a given series converges and for determining its limit if it does converge. See also progressionprogression,
in mathematics, sequence of quantities, called terms, in which the relationship between consecutive terms is the same. An arithmetic progression is a sequence in which each term is derived from the preceding one by adding a given number, d,
.

## Series

in botany, a taxonomic category intermediate between section and species. The series is the first superspecies category and is usually designated by an adjective in the plural form. Closely related geographic races of plants having a normal sexual cycle of development and a common origin form a species series. The concept of series, which played a notable role in the study of plant species, was elaborated in the early 20th century by V. L. Komarov. Geographic races are united in series not according to morphological data but according to phylogenetic data. Hence, this method provides an idea of the course of evolution and makes it possible to “reconstruct that natural process of differentiation of organisms by means of divergence. … which lies at the basis of the process of species formation” (V. L. Komarov, Izbr. soch., vol. 1, 1945, p. 195).

## series

[′sir·ēz]
(analytical chemistry)
A group of results of repeated analyses completed by using a single analytical method on samples of a homogeneous substance.
(electricity)
An arrangement of circuit components end to end to form a single path for current.
(geology)
A number of rocks, minerals, or fossils that can be arranged in a natural sequence due to certain characteristics, such as succession, composition, or occurrence.
A time-stratigraphic unit, below system and above stage, composed of rocks formed during an epoch of geologic time.
(mathematics)
An expression of the form x1+ x2+ x3+ ⋯, where xi are real or complex numbers.
(spectroscopy)
A collection of spectral lines of an atom or ion for a set of transitions, with the same selection rules, to a single final state; often the frequencies have the general formula [R /(a + c1)2] - [R /(n + c2)2], where R is the Rydberg constant for the atom, a and c1 and c2 are constants, and n takes on the values of the integers greater than a for the various lines in the series.

## map series

A group of maps or charts usually having the same scale and cartographic specifications and used for the same general purposes. Each sheet is appropriately identified by the producing agency as belonging to the same series. Also called a series.

## series

1. Maths the sum of a finite or infinite sequence of numbers or quantities
2. Electronics
a. a configuration of two or more components connected in a circuit so that the same current flows in turn through each of them (esp in the phrase in series)
b. (as modifier): a series circuit
3. Geology a stratigraphical unit that is a subdivision of a system and represents the rocks formed during an epoch
References in classic literature ?
Such a birth requires, as its antecedents, not only a series of carefully arranged intermarriages, but also a long, continued exercise of frugality and self-control on the part of the would-be ancestors of the coming Equilateral, and a patient, systematic, and continuous development of the Isosceles intellect through many generations.
The other alternative," said the Earl, "would be a diminuendo series of repetitions of the same type.
The variation from this plan produced a series of cross purposes, disastrous to the establishment, and detained Mr.
It was then, as it is to-day, an irregular trapezoid, bordered on one side by the quay, and on the other three by a series of lofty, narrow, and gloomy houses.
Had Napoleon's aim been to destroy his army, the most skillful strategist could hardly have devised any series of actions that would so completely have accomplished that purpose, independently of anything the Russian army might do.
For this new edition adds to the original merits of the work the very substantial charm of abundant illustrations, first-rate in subject and execution, and of three kinds--copper-plate likenesses of actors and other personages connected with theatrical history; a series of delicate, picturesque, highly detailed woodcuts of theatrical topography, chiefly the little old theatres; and, by way of tail-pieces to the chapters, a second series of woodcuts of a vigour and reality of information, within very limited compass, which make one think of Callot and the German [76] "little masters," depicting Garrick and other famous actors in their favourite scenes.
As he stood there measuring the distance to the opposite side and wondering if he dared venture so great a leap, there broke suddenly upon his startled ears a piercing scream which diminished gradually until it ended in a series of dismal moans.
It was very high at first, descending gradually until it ended in a series of dismal moans.
Her son (of whom I feel truly ashamed to be obliged to speak again so soon) made an effort to extricate his mother--involved himself in a series of pecuniary disasters, which commercial people call, I believe, transactions--struggled for a little while to get out of them in the character of an independent gentleman--failed--and then spiritlessly availed himself of the oleaginous refuge of the soap and candle trade.
After several months of preparation and an expenditure of a million dollars all was in readiness, and a series of tremendous explosions occurred on the earth and in the sky.
As the fashion was, he wrote to her a series of sonnets, in one of which we learn that her name was Elizabeth.
Next, after the Fable of the Hawk and Nightingale, which serves as a condemnation of violence and injustice, the poet passes on to contrast the blessing which Righteousness brings to a nation, and the punishment which Heaven sends down upon the violent, and the section concludes with a series of precepts on industry and prudent conduct generally.

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