Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus III
Topic: Sequences and Infinite Series
Subtopic: Alternating Series

Overview

Alternating series are ones where the signs on the terms in the series alternate signs (eg. positive, negative, positive, etc.) They can be quite interesting and often have surprising results. For instance, divergent series where the terms are all positive are not necessarily divergent when the signs alternate. The alternating series test is an excellent choice for determining the convergence or divergence of an alternating series.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 11.8.1 Recognize if a series is alternating
• 11.8.2 Write an alternating series in summation notation
• 11.8.3 Know that the Alternating Harmonic Series is (conditionally) convergent to ln2
• 11.8.4 Understand the conditions necessary to apply the alternating series test and know the types of series for which the alternating series test is a good choice
• 11.8.5 Know how to use the alternating series test accurately to determine the convergence or divergence of an alternating series
• 11.8.6 Understand when the alternating series test is inconclusive
• 11.8.7 Understand the remainder in the alternating series test and be able to use the remainder formula to find it for a given alternating series

Terminology

Terms you should be able to define: alternating series, alternating series test, remainder in alternating series

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Alternating Series Test

Selwyn Hollis's Video Calculus:
Alternating Series and Absolute Convergence

Patrick JMT Just Math Tutorials:
Alternating Series
Alternating Series - More Examples
Alternating Series - Estimation Theorem

More tutorial videos if you need them are listed at James Sousa's MathIsPower4U - Calc II. Scroll down middle column to "Infinite Series" for related titles.