Chapter 10: Convergence of Series

In Chapter 9, you discovered techniques to determine the sum of infinite geometric series and infinite telescoping series, when they converge. But what about sums of series that are neither geometric nor telescoping? In this chapter you will develop a variety of tools that can be used to determine if other types of series will converge or diverge.

You will also simulate an epidemic crisis in your class to examine differential equations that model the rate that a disease spreads amongst a fixed population.

Finally, you will use tangent lines and other polynomials, to approximate values of non-polynomial functions. 

Chapter Goals

Learn tests for determining
convergence or divergence of
infinite series.

Learn how to approximate a
function using a polynomial.

Use logistic curves to model
change in a fixed population.

Chapter Outline

Section 10.1

You will test an infinite series for convergence or divergence by using the Divergence, Alternating Series, Integral, p-Series, Comparison, Limit Comparison, and/or Ratio Tests.

Section 10.2

You will use logistic functions to model how change occurs in a fixed population. You will solve logistic equations by using past integration techniques in new applications.

Section 10.3

You will analyze how a function can be approximated by using a polynomial.

Section 10.4

You will determine whether an infinite series is conditionally convergent, absolutely convergent, or divergent; and explore some interesting characteristics about each case.