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Chapter 1 installment AND series In this chapter we depart hash out somewhat in?nite serial publication, which are sums that involve in?nitely many a(prenominal) wrong. In?nite series play a fundamental fictional character in both mathematics and science for example, to approximate trigonometric bleeds and logarithms, to wreak di?erential equations, to evaluate di?cult integrals, to create new modus operandis, and to take in numerical model of physical laws. Learning Outcomes At the oddity of this topic, pupil are able to: a. de?ned and di?erence between the rate and the series, b. ?nd the make of age, c. de preconditionine the convergence and divergence of sequence and series utilise convergence and divergence test. 1.1 Sequence De?nition 1.1 An in?nite sequence, or more just now a sequence, is an unending successiveness of numbers, called lines. Or in different words, a sequence of truly numbers is a real-valued function whose ambit is the c lique of innate numbers or integers. 1 2 CHAPTER 1. SEQUENCE AND SERIES Terms have a de?nite order; that is a ?rst marches a1 , a second enclosure a2 , a trio term a3 , a fourth term a4 , and so on. typically be written as a1 , a2 , a3 , a4 , . . . Speci?c examples: 1, 2, 3, 4, . . . 2, 4, 6, 8, . . . 1 1 1 1, , , , . . . 2 3 4 1, ?1, 1, ?1, . . .

Each of these sequence has a de?nite pattern that makes it easy to generate additional terms - if birth follow the same pattern as displayed terms. However, much(prenominal) patterns can be deceiving - better to have a mold of formula for generating the terms. peerless way to doing this is - look for a function that relat es each term in the sequence to its term num! ber. The domain of a sequence is the set of positive integers or the set of nonnegative integers. pillowcase 1.2 In each part, ?nd the abundant general term of the sequence. 1 2 3 4 , , , ,... 2 3 4 5 1 1 1 1 , , , ,... 2 4 8 16 1 ?2 3 ?4 , , , ,... 2 3 4 5 a. b. c. d. 1, 3, 5, 7, . . . Solution: 1.1. SEQUENCE Commonly the general term entrust be expressed in...If you want to get a abounding essay, order it on our website: OrderEssay.net

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