Lecture 8-1 - 8.1 Sequences Defn Sequence A sequence(or...

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Unformatted text preview: 8.1 - Sequences Defn. Sequence A sequence (or infinite sequence) is a list of numbers written in a definite order. It is a function whose domain is the positive integers. We denote a sequence by Examples of Sequences 1. 1 , 2 , 3 ,...,n,... 2. a n = (- 1) n +1 · 1 n 3. a n = cos( πn ) Example 1 Find a formula for { a n } . 1. 2 , 6 , 10 , 14 ,... 2. 0 , 3 , 8 , 15 , 24 ,... 1 Recursively Defined Sequences Sequences can often be defined recursively by giving 1. 2. Examples of Recursively Defined Sequences 1. a 1 = 1 a n = a n- 1 + 1 2. The Fibonacci Sequence: a 1 = 1, a 2 = 1 a n +1 = a n + a n- 1 2 Convergence or Divergence of a Sequence Defn. Sequence Convergence or Divergence A sequence { a n } converges if where L is a finite number, called the limit of the sequence. If { a n } does not converge (i.e. the limit DNE), then it diverges . Examples Determine if the following sequences converge or diverge. If they converge, state the limit of the sequence....
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This note was uploaded on 03/03/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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Lecture 8-1 - 8.1 Sequences Defn Sequence A sequence(or...

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