Chapter 11: Sequences, Series, and Power Series

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Course

MATH163 (Calculus III)

Overview

This chapter covers Sequences, Series, and Power Series from Stewart Calculus 9th Edition.

Each section contains:

Sections

Section 11.1: Sequences

Skill Description Difficulty
Limits of Sequences Sequences, Series, and Power Series Intermediate
Properties of Sequences Sequences, Series, and Power Series Intermediate
Sequences and Notation Sequences, Series, and Power Series Intermediate

Section 11.2: Series

Skill Description Difficulty
Geometric Series Sequences, Series, and Power Series Intermediate
Infinite Series Sequences, Series, and Power Series Intermediate
Telescoping Series Sequences, Series, and Power Series Intermediate
Test for Divergence Sequences, Series, and Power Series Intermediate

Section 11.3: The Integral Test and Estimates of Sums

Skill Description Difficulty
Remainder Estimates Sequences, Series, and Power Series Intermediate
The Integral Test Sequences, Series, and Power Series Intermediate

Section 11.4: The Comparison Tests

Skill Description Difficulty
Direct Comparison Test Sequences, Series, and Power Series Intermediate
Limit Comparison Test Sequences, Series, and Power Series Intermediate

Section 11.5: Alternating Series and Absolute Convergence

Skill Description Difficulty
Absolute vs Conditional Convergence Sequences, Series, and Power Series Intermediate
Alternating Series Test Sequences, Series, and Power Series Intermediate

Section 11.6: The Ratio and Root Tests

Skill Description Difficulty
The Ratio Test Sequences, Series, and Power Series Intermediate
The Root Test Sequences, Series, and Power Series Intermediate

Section 11.7: Strategy for Testing Series

Skill Description Difficulty
Series Testing Strategy Sequences, Series, and Power Series Intermediate

Section 11.8: Power Series

Skill Description Difficulty
Power Series Sequences, Series, and Power Series Intermediate
Radius and Interval of Convergence Sequences, Series, and Power Series Intermediate

Section 11.9: Representations of Functions as Power Series

Skill Description Difficulty
Finding Power Series Representations Sequences, Series, and Power Series Intermediate
Manipulating Power Series Sequences, Series, and Power Series Intermediate

Section 11.10: Taylor and Maclaurin Series

Skill Description Difficulty
Taylor Polynomials Sequences, Series, and Power Series Intermediate
Taylor and Maclaurin Series Sequences, Series, and Power Series Intermediate
Taylor’s Inequality Sequences, Series, and Power Series Advanced

Section 11.11: Applications of Taylor Polynomials

Skill Description Difficulty
Applications of Taylor Series Sequences, Series, and Power Series Intermediate
Approximating Functions Sequences, Series, and Power Series Intermediate

Prerequisites

Before starting Chapter 11, review relevant prerequisite skills from earlier chapters.

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