8.4 Other Convergence Tests

Mathematica script by Chris Parrish,

cparrish@sewanee.edu

Sources and references for some of these problems include

James Stewart, "Calculus: Concepts and Contexts," Second Edition, Brooks/Cole, 2001

Deborah Hughes-Hallett, Andrew M. Gleason, et. al., "Calculus," Second Edition, John Wiley & Sons, 1998

Robert Fraga, ed., "Calculus Problems for a New Century," The Mathematical Association of America, 1993

Selwyn Hollis, "CalcLabs with Mathematica" for Stewart's "Single Variable Calculus, Concepts and Contexts, Second Edition," Brooks/Cole, 2001

Alternating Series

In an alternating series the signs of the terms alternate.

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The three requirements of the alternating series test are satisfied for this series, so it converges, in spite of its resemblence to the divergent harmonic series.

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This plot suggests that convergence, and even indicates why the criteria of the alternating series test will guarantee convergence of an alternating series. The oscillations about the limit point must tend to zero.

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Created by Mathematica (May 5, 2004)