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: Ratio Test & Root Test

Overview

The ratio test and root test are two of the most common tests to use to determine if a series is convergent or divergent. The ratio test involves taking the limit of a ratio and the root test involves taking the limit of a root. The ratio test is advisable when the n-th term of the series involves n!, a^n, nor n^n where a is a constant. The root test is advisable when the n-th term of the series involves a power containing n.

Objectives

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

• 11.6.1 Understand the conditions necessary to apply the ratio test and know the types of series for which the ratio test is a good choice
• 11.6.2 Know how to use the ratio test accurately to determine the convergence or divergence of a series
• 11.6.3 Understand when the ratio test is inconclusive
• 11.6.4 Understand the conditions necessary to apply the root test and know the types of series for which the root test is a good choice
• 11.6.5 Know how to use the root test accurately to determine the convergence or divergence of a series
• 11.6.6 Understand when the root test is inconclusive

Terminology

Terms you should be able to define: ratio test, root test, limit "L" from the ratio or root test, inconclusive

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Ratio Test and Root Test

Selwyn Hollis's Video Calculus:
Comparison Tests (including the ratio and root tests)

Patrick JMT Just Math Tutorials:
Ratio Test - Example 1
Ratio Test - Example 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.