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Chapter 9 Infinite Series

Infinite Series(9)

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Page 1: Infinite Series(9)

Chapter 9

Infinite Series

Page 2: Infinite Series(9)

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Definition of the Limit of a Sequence and Figure 9.1

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Theorem 9.1 Limit of a Sequence

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Theorem 9.2 Properties of Limits of Sequences

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Theorem 9.3 Squeeze Theorem for Sequences

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Theorem 9.4 Absolute Value Theorem

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Definition of a Monotonic Sequence

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Definition of a Bounded Sequence

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Theorem 9.5 Bounded Monotonic Sequences

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Definitions of Convergent and Divergent Series

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Theorem 9.6 Convergence of a Geometric Series

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Theorem 9.7 Properties of Infinite Series

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Theorem 9.8 Limit of nth Term of a Convergent Series

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Theorem 9.9 nth-Term Test for Divergence

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Theorem 9.10 The Integral Test

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Theorem 9.11 Convergence of p-Series

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Theorem 9.12 Direct Comparison Test

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Theorem 9.13 Limit Comparison Test

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Theorem 9.14 Alternating Series Test

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Theorem 9.15 Alternating Series Remainder

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Theorem 9.16 Absolute Convergence

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Definitions of Absolute and Conditional Convergence

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Theorem 9.17 Ratio Test

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Theorem 9.18 Root Test

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Guidelines for Testing a Series for Convergence or Divergence

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Summary of Tests for Series

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Summary of Tests for Series (cont’d)

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Definitions of nth Taylor Polynomial and nth Maclaurin Polynomial

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Theorem 9.19 Taylor's Theorem

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Definition of Power Series

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Theorem 9.20 Convergence of a Power Series

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Theorem 9.21 Properties of Functions Defined by Power Series

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Operations with Power Series

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Theorem 9.22 The Form of a Convergent Power Series

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Definitions of Taylor and Maclaurin Series

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Theorem 9.23 Convergence of Taylor Series

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Guidelines for Finding a Taylor Series

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Power Series for Elementary Functions