Lesson 6: 11.6 Absolute Convergence and the Ratio and Root Tests
Duration of Days: 3
Lesson Objective
Students will be able to determine whether a series is absolutely convergent, conditionally convergent, or divergent by using either the Ratio Test or the Root Test.
- What is the difference between "absolutely convergent" and "conditionally convergent"?
- Under what "condition" is a series "conditionally convergent"?
- How is the Ratio Test related to the Comparison Test?
- absolutely convergent
- conditionally convergent
- Ratio Test
- Root Test
(determining the convergence of a series using the Ratio and Root Tests)
- To determine whether an infinite series is absolutely convergent, conditionally convergent, or divergent using the Ratio Test or the Root Test.
- DOK Levels 1-4
- calculating total future value of annuities and investments
- calculating materials needed for construction
- radioactive decay and population growth
Students may occasionally find it tricky to simplify the limit once they have set up the Ratio Test. Also, the conclusions of the Ratio and Root Tests can be confused with the conclusion of the p-series and/or the Test for Divergence.
Homogeneous grouping and whole class discussion
section assessment
problems assigned from book