Infinite Series(9)

Chapter 9

Infinite Series

Definition of the Limit of a Sequence and Figure 9.1

Theorem 9.1 Limit of a Sequence

Theorem 9.2 Properties of Limits of Sequences

Theorem 9.3 Squeeze Theorem for Sequences

Theorem 9.4 Absolute Value Theorem

Definition of a Monotonic Sequence

Definition of a Bounded Sequence

Theorem 9.5 Bounded Monotonic Sequences

Definitions of Convergent and Divergent Series

Theorem 9.6 Convergence of a Geometric Series

Theorem 9.7 Properties of Infinite Series

Theorem 9.8 Limit of nth Term of a Convergent Series

Theorem 9.9 nth-Term Test for Divergence

Theorem 9.10 The Integral Test

Theorem 9.11 Convergence of p-Series

Theorem 9.12 Direct Comparison Test

Theorem 9.13 Limit Comparison Test

Theorem 9.14 Alternating Series Test

Theorem 9.15 Alternating Series Remainder

Theorem 9.16 Absolute Convergence

Definitions of Absolute and Conditional Convergence

Theorem 9.17 Ratio Test

Theorem 9.18 Root Test

Guidelines for Testing a Series for Convergence or Divergence

Summary of Tests for Series

Summary of Tests for Series (cont’d)

Definitions of nth Taylor Polynomial and nth Maclaurin Polynomial

Theorem 9.19 Taylor's Theorem

Definition of Power Series

Theorem 9.20 Convergence of a Power Series

Theorem 9.21 Properties of Functions Defined by Power Series

Operations with Power Series

Theorem 9.22 The Form of a Convergent Power Series

Definitions of Taylor and Maclaurin Series

Theorem 9.23 Convergence of Taylor Series

Guidelines for Finding a Taylor Series

Power Series for Elementary Functions

Infinite Series(9)

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