10.6 Comparison Tests for Convergence
1 min readβ’june 18, 2024
AP Calculus AB/BCΒ βΎοΈ
279Β resourcesSee Units
.png?alt=media&token=c9b56758-c8bf-40c4-8a4f-0522d9a8a009)
Intro to the Comparison Tests
When you canβt use the integral test, you can see if the series looks like a geometric or p-series. From this, you can use these similarities to determine whether a series converges or diverges.
What is the Direct Comparison Test?
The Direct Comparison Test is as follows:
.png?alt=media&token=858be3e7-e27b-4d51-bee4-6478d3bfa2f2)
.png?alt=media&token=f6e51a1e-607b-4536-ad55-372fe3b9e337)
.png?alt=media&token=c3c358fa-e71f-4ba9-aa16-fc65e6e70584)
What is the Limit Comparison Test?
The Limit Comparison Test is as follows:
.png?alt=media&token=9dfd56c4-0526-43e9-b6a9-5e1726e8a835)
.png?alt=media&token=0149c335-a837-4780-ae6f-73f434fa929d)
.png?alt=media&token=b89aa76b-0ad0-4dfa-a3d2-7c858e0beac0)
Problems
1. State the two comparison tests. What are the differences between them?
Determine whether the following series converge or diverge.
.png?alt=media&token=280ebc70-8df0-4989-ab0a-5027bee92c28)
Browse Study Guides By Unit
πUnit 1 β Limits & Continuity
π€Unit 2 β Fundamentals of Differentiation
π€π½Unit 3 β Composite, Implicit, & Inverse Functions
πUnit 4 β Contextual Applications of Differentiation
β¨Unit 5 β Analytical Applications of Differentiation
π₯Unit 6 β Integration & Accumulation of Change
πUnit 7 β Differential Equations
πΆUnit 8 β Applications of Integration
π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
βΎUnit 10 β Infinite Sequences & Series (BC Only)
πStudy Tools
π€Exam Skills
Fiveable
Resources
Β© 2024 Fiveable Inc. All rights reserved.