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Unformatted text preview: Math 1432 THINK: Which of the following is not an anagram of a boat or ship? LONG ADO LEAN LOG SET VEER SEA TERM GET FAIR Important examples: ∞ ∫ 1 dx x ∞ = = ∑ n 1 1 n ∞ ∫ 2 1 dx x ∞ = = ∑ 2 n 1 1 n ∞ ∫ 1 2 1 dx x 11.1 Infinite Series General Properties: If ∞ = ∑ k k 0 a converges and ∞ = ∑ k k 0 b converges, then ( 29 ∞ = + ∑ k k k 0 a b converges. If ∞ = ∑ k k 0 a converges, then ∞ = α ∑ k k 0 a converges. Ex. 1 Does ∞ =   + ∑ n 1 1 1 2n 1 2n 1 converge or diverge? Telescoping Series: A series such as  + + + + 1 1 1 1 1 1 1 1 2 2 3 3 4 4 5 ... is called a telescoping series because it collapses to one term or a few terms. If a series collapses to a finite sum, then it converges. Ex. 2. Does the series 1 – 1 + 1 – 1 + 1 … converge or diverge?...
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This note was uploaded on 03/06/2011 for the course MATH 1432 taught by Professor Morgan during the Spring '08 term at University of Houston.
 Spring '08
 morgan
 Math, Infinite Series

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