LESSON NOTES MENU
Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
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
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
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis

Course: Calculus III
Topic: Sequences and Infinite Series
Subtopic: Absolute and Conditional Convergence

Overview

As we have seen with the alternating harmonic series (convergent) and the harmonic series (divergent), removing the alternating signs on a convergent series does not necessarily render it convergent too. This is an example of conditional convergence. In this section we study series that converge conditionally and those that converge absolutely. Absolute convergence (ie. involving the absolute value of the terms in the series) implies convergence. Lots of new terminology!

Objectives

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

• 11.9.1 Know what it means for a series to be absolutely convergent or conditionally convergent
• 11.9.2 Understand what it means for absolute convergence to imply convergence
• 11.9.3 Use the Absolute Convergence Theorem where appropriate to analyze a sequence
• 11.9.4 Able to use a general strategy to determine which test is best to use to analyze the convergence or divergence of a series, in other words, to see the "big picture" in the analysis of any infinite series

Terminology

Define: absolute convergence, converging absolutely, conditional convergence, converging conditionally, general strategy using tests on series

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Absolute Convergence and Strategy for Series

Patrick JMT Just Math Tutorials:
Absolute Convergence & Conditional Convergence
Strategy for Testing Series - Practice Problems

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.