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
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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

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.