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Chapter 9
Infinite Series
Copyright © Houghton Mifflin Company. All rights reserved. 9-2
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