📚

 > 

♾️ 

 > 

10.8 Ratio Test for Convergence

1 min readjune 18, 2024


AP Calculus AB/BC ♾️

279 resources
See Units

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(565).png?alt=media&token=dfcca525-b3a8-48f7-b6d7-d72877aec6c8
There are many tests that you have learned for this course, and we are headed to the final one, the ratio test, which is useful for series with exponentials or factorials.

What is the Ratio Test?

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(771).png?alt=media&token=3277d7bb-13ea-4e82-9c38-1fc534306713
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(772).png?alt=media&token=39543e52-7a09-43bb-947b-767e22143a09
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(774).png?alt=media&token=a39caa7b-6a31-4a27-ab8a-8d72260a23f2

Review Flowchart

Now that we have completed all the tests that you need to know for the AP Calculus BC test, here is a flowchart showing how to use the tests (ignore the Taylor Series, which we will talk about later, and the root test, which is not required for this course).
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fseries-convergence-divergence-flow-chart.jpg?alt=media&token=62fd34b9-adac-49ac-9afa-61ac0b8433f2
For a better resolution, check out this link.

Problems

1. State the ratio test.
Determine if the following series converge or diverge.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(776).png?alt=media&token=6fa17828-fc04-4dc7-b717-3aa943e24d29
Browse Study Guides By Unit
👑Unit 1 – Limits & Continuity
🤓Unit 2 – Fundamentals of Differentiation
🤙🏽Unit 3 – Composite, Implicit, & Inverse Functions
👀Unit 4 – Contextual Applications of Differentiation
Unit 5 – Analytical Applications of Differentiation
🔥Unit 6 – Integration & Accumulation of Change
💎Unit 7 – Differential Equations
🐶Unit 8 – Applications of Integration
🦖Unit 9 – Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
📚Study Tools
🤔Exam Skills