2224-Sec8_1-HWT

2224-Sec8_1-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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Math 2224 Multivariable Calculus – Chapter 8 Infinite Sequences and Series Sec. 8.1: Sequences I. Sequence A. Definitions 1. Def n : A sequence is a list of numbers written in a definite order a 1 , a 2 , a 3 ,..., a n ,... where a 1 = 1 st term , a 2 = 2 nd term , a 3 = 3 rd term , a n = n th term and n =index of a n . 2. An infinite sequence of numbers is a function whose domain is ! + (the set of positive integers). You can denote the sequence by its n th term a n { } or a n { } n = 1 ! . B. Examples 1. 1,2,3,. .., n ,... n { } n = 1 ! a n = n 2. 1, ! 1 2 , 1 3 , ! 1 4 ,... 3. a n = cos( ! n ) 4. a n = 3 n + 1 n + 2 5. a n = e n 2 n C. Graphical Representation of Sequences 1. There are two ways to represent sequences graphically. The first method represents the first few terms on the real axis. The second method represents the first few terms as points on the graph of the function defining the sequence. The function is defined only on integer inputs and the points on the graph are (1, a 1 ), (2, a 2 ), (3, a 3 ),. .., ( n , a n ),. .. 2. Example - # 2 from above a 2 a 4 a 5 a 3 a 1
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II. Convergence and Divergence A. Definition 1. Def n : The sequence a n { } converges to the number L if for every positive number
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This note was uploaded on 04/05/2008 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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2224-Sec8_1-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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