Calculus II Workbook For Dummies

Chapter 16

Convergent and Divergent Series

IN THIS CHAPTER

Understanding the nth-term test for divergence

Using the direct comparison test to show convergence and divergence

Applying the limit comparison test to a series

Using the integral test to decide whether a series is convergent or divergent

Applying the ratio test to a series with exponents and factorials

Using the root test when a series has an exponent of n

In this chapter, you expand your understanding of infinite series with a variety of tests for convergence or divergence.

To begin, you see how the nth-term test provides an easy and intuitive way to show that many series are divergent. Then, you see how two comparison tests — the direct comparison test and the limit comparison test — allow you to use information about a series that you know to find out whether a new series is convergent or divergent.

Next, you break out ...