INFINITE SERIES

Sequences & Series

Intuitive discussion of sequences and series

Discussion of sequences

Discussion on series

Visualizing an infinite series using a trapezoid
The commutative law doesn't hold for certain series
Understanding series

Graphs a_n and the sequence of partial sums applet

Sequence applet

A discovery approach to introducing infinite series worksheet

Part 2 of the discovery approach to infinite series worksheet
How do your favorite sequences stack up? Worksheet

Convergence of Sequences

Series and Convergence

Geometric Series

Introduction to series; starts with geometric series
Introduction to Infinite Series Worksheet
Series and Convergence

nth Term Test
Series applet

The Integral Test and p-Series

Integral Test

Integral test applet

The Integral Test and p-Series

Comparisons of Series

Direct Comparison Test

Comparison Test applet

Limit Comparison Test

Limit comparison test applet

Comparison of Series

Alternating Series

Working with Alternating Series

A divergent alternating series whose terms go to zero
Alternating Series Test applet

Absolute Convergence

The Ratio and Root Tests

Ratio Test

Ratio Test applet

Convergence of Series

Which test should be used?

Taylor Polynomials and Approximations

Finding Taylor Series

Taylor Polynomial applet

Tutorial on Taylor polynomials

Problems on Taylor and MacLaurin Series
Problems -- Graphically find a Taylor Expansion for a function

Taylor Series and polynomials applet

A function which doesn't equal its Taylor series, part 1

A function which doesn't equal its Taylor series, part 2

Why do Taylor Series work?
What can we do with Taylor series?

Applications of Series

If Only Every Function were a Polynomial lesson
Find the error
Taylor's Theorem

Lecture on Taylor's Theorem on YouTube
Lagrange Remainder applet

Power Series

Power Series applets

Tutorial on power series
Differentiation & Integration of power series
Power Series PowerPoint (Find 9.1)

Radius of Convergence
Power Series and Interval of Convergence applet

Testing Convergence at Endpoints

Representation of Functions by Power Series
Taylor and Maclaurin Series

Applications of Taylor Series

Summaries and Review Problems

Review problems