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ss_11_1 - Section 11.1 Sequences For most purposes, one can...

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Unformatted text preview: Section 11.1 Sequences For most purposes, one can consider a sequence to be a list of numbers. The numbers in the list are called terms of the sequence. Even though sequences are simple objects, they are important mathematical tools. There are many ways to designate sequences. We list only a few of the most common notations below. Notation for a sequence: { a 1 , a 2 , a 3 , } { a n } ( a n ) Examples of sequences: (1) { 1 , 2 , 3 , } (2) { (- 1) n- 1 } = { 1 ,- 1 , 1 ,- 1 , } (3) { 3 , 1 , 4 , 1 , 7 , } (4) { n- 1 n } = { , 1 2 , 2 3 , } (5) a 1 = 1, a n = 2 a n- 1 when n 2 Note: The sequence { (- 1) n } is called an alternating sequence . (- 1) n =- 1 when n is odd and (- 1) n = 1 when n is even. By definition, a sequence is a function defined on the set of positive integers . When the sequence is designated by { a 1 , a 2 , a 3 , } and the function defining the sequence is named f , then f (1) = a 1 , f (2) = a 2 , f (3) = a 3 , . The subscripts of a 1 , a 2 are the elements of the domain of f ....
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ss_11_1 - Section 11.1 Sequences For most purposes, one can...

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