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: Divergence Test (a.k.a. n-th Term Test)

Overview

To determine if an infinite series is convergent or divergent, there are a variety of "tests" we can use. The first of these is the Divergence Test, also known as the n-th Term Test. Be careful to use this test properly. If the limit of the sequence of terms in the series is not zero, then the series is divergent. But if the limit of the sequence of terms is zero, the test is inconclusive and we have to find a different method of determining if the series is convergent or divergent.

Objectives

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

• 11.4.1 Use the n-th Term Test to determine if a series is divergent
• 11.4.2 Understand the limitations of the n-th Term Test, in particular when it is inconclusive
• 11.4.3 Know that the Harmonic Series is divergent

Terminology

Define: n-th term, n-th term test, divergence test theorem

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Convergence/Divergence

Patrick JMT Just Math Tutorials:
Geometric Series and the Test for Divergence - Part 1
Geometric Series and the Test for Divergence – Part 2

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.