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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
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Course: Calculus III
Topic: Sequences and Infinite Series
Subtopic: n-th Term Test (a.k.a. Divergence 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 n-th Term Test, also known as the Divergence 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:

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.