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 ..

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 ..

Linear equations/inequalities Monomials and polynomials Factoring second and third degree polynomials Rational expressions/functions Quadratic equations Quadratic functions Exponents, factors, variation, exponential growth/decay Hypothesis, counterexamples Correlation for data Patterns, ..