Chapter 10: Infinite Series

Packets

10.1 Power Series

10.2 Taylor Series

10.3 Taylor's Theorem

10.4 Radius of Convergence

10.5 Testing Convergence at Endpoints

Review

Chapter Summary

Packets

Chapter 10 Packet Numbered.pdf

10.1 Power Series

Mastery Objectives

Students will be able to apply properties of geometric series
Students will be able to differentiate, integrate, or substitute into a known power series in order to find additional power series representations.

Notes

10.1 Notes All.pdf

Book Problems

#s 2-6, 11,14,15,18,21,23,25,27,31,35,44,48,54,55

Videos

Infinite Series Introduction

Tests for Convergence

Power Series Introduction

Creating New Power Series from Known Ones

Differentiating and Integrating Power Series

Geometric Power Series and Integration

10.2 Taylor Series

Mastery Objectives

Students will be able to use derivatives to find Maclaurin series or Taylor series generated by a differentiable function

Notes

10.2 Notes.pdf

Book Problems

#2,3,14,16,21,23,24,25,26,32,35,37-43

Videos

Intro to Taylor Series

Taylor Series for Sin(x)

Taylor Series Centered at x = 0 (aka Maclaurin Series)

Taylor Series Centered at x = a

10.3 Taylor's Theorem

Mastery Objectives

Students will be able to approximate a function with a Taylor polynomial
Students will be able to analyze the truncation error of a series using graphical methods or the Remainder Estimation Theorem.

Notes

10.3 Notes.pdf

Book Problems

#’s7,10,19,21,23,24,27,32,33,34,36,41,QQAP1-4

Videos

The Truncation Error for Taylor Polynomials

Analyzing Taylor Polynomial Errors Graphically

Taylor's Theorem and the Remainder Estimation Theorem

Max Error for e^x Maclaurin Polynomial Graphically

Max Error of Sin(x) Maclaurin Polynomial Graphically

Remainder Estimation Theorem Interval Problem

Alternating Series Versus Remainder Estimation Theorem

10.4 Radius of Convergence

Mastery Objectives

Students will be able to use the nth-Term Test, the Direct Comparison Test, and the Ratio Test to determine the convergence of divergence of a series of numbers or the radius of convergence of a power series.

Notes

10.4 Notes.pdf

Book Problems

#s 1,4,5,9,11,14,17,23,28,29,33,35,44,49,51,59

Videos

Power Series, Nth Term Test and Comparison Tests

The Ratio Test and Absolute Convergence

The Ratio Test and Power Series

The Nth Root Test

10.5 Testing Convergence at Endpoints

Mastery Objectives

Students will be able to use the Integral Test and the Alternating Series Test to determine the convergence or divergence of a series of numbers.
Students will be able to determine the convergence or divergence of p-series, including the harmonic series.
Students will be able to determine the absolute convergence, conditional convergence, or divergence of a power series at the endpoints of its interval of convergence.