Chapter 1

Infinite Series

Definition of the Limit of a Sequence

Limit of a Sequence

Properties of Limits of Sequences

Squeeze Theorem for Sequences

Absolute Value Theorem

Definition of a Monotonic Sequence

Definition of a Bounded Sequence

Bounded Monotonic Sequences

Definitions of Convergent and Divergent Series

Convergence of a Geometric Series

Properties of Infinite Series

Limit of nth Term of a Convergent Series

nth-Term Test for Divergence

The Integral Test

Convergence of p-Series

Direct Comparison Test

Limit Comparison Test

Alternating Series Test

Alternating Series Remainder

Absolute Convergence

Definitions of Absolute and Conditional Convergence

Ratio Test

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

Taylor's Theorem

Definition of Power Series

Convergence of a Power Series

Properties of Functions Defined by Power Series

Operations with Power Series

The Form of a Convergent Power Series

Definitions of Taylor and Maclaurin Series

Convergence of Taylor Series

Guidelines for Finding a Taylor Series

Power Series for Elementary Functions