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Chapter 1 installment AND serial publication In this chapter we depart argue somewhat in?nite serial, which are sums that involve in?nitely many a(prenominal) wrong. In?nite series play a fundamental mapping 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 ca-ca numerical model of physical laws. Learning Outcomes At the decision of this topic, pupil are able to: a. de?ned and di?erence between the rate and the series, b. ?nd the make of eon, c. de limitine 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 succession of numbers, called edges. Or in different words, a sequence of veridical numbers is a real-valued function whose ambit is the clique of inwrought nu mbers or integers. 1 2 CHAPTER 1. SEQUENCE AND SERIES Terms have a de?nite order; that is a ?rst depot a1 , a second precondition 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 absorb 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. atomic number 53 way to doing this is - look for a function that relates each t erm in the sequence to its term number. The! domain of a sequence is the set of positive integers or the set of nonnegative integers. pillow slip 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 volition be expressed in...If you want to get a integral essay, order it on our website: OrderEssay.net

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