Lecture 8-5 - lim n n n = 3 Examples Determine whether the...

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8.5 - The Ratio and Root Tests The Ratio Test Suppose a n is a series of positive terms and lim n →∞ a n +1 a n = L. Then, 1. 2. 3. Note: Examples Determine whether the following series converge or diverge. 1. X n =1 5 n n 3 1
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2. X n =1 n 2 n ( n + 1)! 3 n n ! 3. X n =1 n + 2 5 n 2 + 3 2
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The Root Test Let a n be such that a n 0 for all n N , where N is some positive integer. Suppose lim n →∞ n a n = ρ. Then, 1. 2. 3. Note: Helpful limit to know when using the Root Test
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Unformatted text preview: lim n n n = 3 Examples Determine whether the following series converge or diverge. 1. X n =1 (ln n ) n n n 2. X n =1 10 n n 10 4 Do. Determine if the following series converge or diverge. 1. X n =1 n 1 2 n 2. X n =1 n ! ln n n ( n + 2)! 5...
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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 8-5 - lim n n n = 3 Examples Determine whether the...

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