history of sequence and series

Sequence : A set of numbers arranged in a definite order according to some definite rule is called a sequence.A sequence is a function whose domain is the set N of natural numbers. Series : Indicated sum of the terms in a sequence is..

A set of numbers arranged in a definite order according to some definite rule is called a sequence. A sequence is a function whose domain is the set N of natural numbers. Indicated sum of the terms in a sequence is called a series. The result of p..

Sequence - A set of numbers arranged in a definite order according to some definite rule is called a sequence. or A sequence is a function whose domain is the set N of natural numbers. It is customary to denote a sequence by a letter 'a' and the image a(n) or..

Introduction - A set of numbers arranged in a definite order according to some definite rule is called a sequence..

Introduction - A set of numbers arranged in a definite order according to some definite rule is called a sequence . Sequences have wide applications. For example, the amount of money in a fixed deposit in a bank, over a number of years increases in a sequence..

Summary - (i) Let X be a set of numbers and f : N n X be a function, then the ordered set {f(1), f(2),...., f(n)} is called a finite sequence in X. (ii) Let X be a set of numbers and f : N X be a function, then the ordered set {f(1), f(2),....} is called an infinite sequence in ..

Indicated sum of the terms in a sequence is called a series. The result of performing the additions is the sum of the series...

Which of the following are true for the series ∑ n=1 ∞ (- 1) n sin ( π n ) ? I. lim n → ∞ sin ( π n ) = 0 II. {sin ( π n )} is a decreasing sequence III. The series is convergent by the Alternating Series Test IV. Alternating ..

There are at least three systems in use for naming alkanes. However, the IUPAC system of nomenclature is used almost universally. According to this system, the first four members of the alkane series have special names related to their history. Thereafter, the alkanes are ..

Limits of sequences, series Continuity, end behavior, asymptotes, limits Regression Law of Sines/Cosines, area formulas Parametric/rectangular forms of functions Vectors Even/odd functions, significant values Functions and operations Conic sections- applications ..