calc test 1 - A and B are series with positive terms. If...

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Indeterminate form, Powers : Geometric Series : *r is the ratio Is convergent if |r| 1 between terms Is divergent if |r| 1 Integral Text: Suppose f is a continuous, positive, decreasing function on [1, ) and let A = f(n). Then the series A is convergent if and only if the improper integral f(x) dx is convergent. In other words: 1. f(x) dx is convergent, then A is convergent. 2. f(x) dx is divergent, then A is divergent P-series test : The P-series is convergent if p 1 and divergent if p 1. Comparison Test : Suppose that A and B are series with positive terms. 1. If B is convergent and A B for all n, the A is also convergent. 2. If B is divergent and A B for all n, then A is also divergent. Limit Comparison Test : Suppose that
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Unformatted text preview: A and B are series with positive terms. If where c is a finite number and c 0, then either both series converge or both diverge. The Alternating Series Test : If the alternating series: Satisfies: 1. B B for all n 2. lim B = 0 then the series is convergent. Ratio Test: 1. If L 1, then the series is absolutely convergent 2. If L 1, then the series is divergent. 3. If L = 1, then the Ratio Test is inconclusive; that is, no conclusion can be drawn about the convergence or divergence of the series using ratio test. Root Test: 1. If L 1, then the series is absolutely convergent 2. If L 1, or L = , then the series is divergent. 3. If L = 1, thatn the Root Test is inconclusive. Power Series Stuff:...
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This note was uploaded on 03/19/2008 for the course M 408 taught by Professor Hodges during the Spring '08 term at University of Texas.

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calc test 1 - A and B are series with positive terms. If...

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