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: Ratio Test & Root Test


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.


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


Define: ratio test, root test, limit "L" from the ratio or root test, inconclusive

Supplemental Resources (required)

Download/Print: Prof. Keely's Summary of Tests for Series

Download/Print: Flowchart: Choosing a Convergence Test for Infinite Series (David Manuel)
or Flowchart: Series Convergence/Divergence (Dennis DeTurck)

Supplemental Resources (reccommended)

It is recommended that you check these out and choose any that you find helpful in deciding which series test to use:

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.