8.6 Notes - AST

# 8.6 Notes AST - finite value As with the Integral Test you may have to use the first derivative to determine if you have a decreasing function

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Calculus II Section 8.6 Alternating Series, Absolute and Conditional Convergence Up to this point most of our series in question have been positive-term series. Now we will consider the convergence and divergence of series with both positive and negative terms. (Although note that we did extend the Ratio and Root Tests in your text to include nonnegative termed series.) Alternating Series An alternating series is one whose terms alternate in sign. Example: Alternating Series Test Let . The alternating series and converge if the following conditions are met: 1) (Note that and therefore does not include the alternating signs.) 2) for all n . (Note that this just means the sequence is decreasing. Once again, it really doesn t have to be decreasing for all n starting at n=1, as long as the sequence is eventually decreasing starting with some

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Unformatted text preview: finite value. As with the Integral Test, you may have to use the first derivative to determine if you have a decreasing function.) Examples: For some series with positive and negative terms, the series formed by taking the absolute value of the terms actually converges. If this happens, then the series with positive and negative terms also converges and we say the series is absolutely convergent. Definition: A series converges absolutely if the corresponding series converges. A series that converges but does not converge absolutely converges conditionally . Examples: Absolute Convergence Test If converges, then converges. Determine whether the following series converge conditionally, converge absolutely, or diverge....
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## This note was uploaded on 01/13/2012 for the course MATH 2564 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.

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8.6 Notes AST - finite value As with the Integral Test you may have to use the first derivative to determine if you have a decreasing function

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