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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
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:

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.