๐Ÿ“š

All Subjects

ย >ย 

โ™พ๏ธย 

AP Calc

ย >ย 

โ™พ

Unit 10

10.8 Ratio Test for Convergence

1 min readโ€ขjune 8, 2020

peter-cao

Peter Cao


AP Calculus AB/BCย โ™พ๏ธ

Bookmarkedย 7.1kย โ€ขย 259ย 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

Was this guide helpful?

Join us on Discord
Thousands of students are studying with us for the AP Calculus AB/BC exam.
join now
Hours Logo
Studying with Hours = the ultimate focus mode
Start a free study session
๐Ÿ” Are you ready for college apps?
Take this quiz and find out!
Start Quiz
Browse Study Guides By Unit
๐Ÿ“†Big Reviews: Finals & Exam Prep
โœ๏ธFree Response Questions (FRQ)
๐ŸงMultiple Choice Questions (MCQ)
โ™พUnit 10: Infinite Sequences and Series (BC Only)
๐Ÿ‘‘Unit 1: Limits & Continuity
๐Ÿค“Unit 2: Differentiation: Definition & Fundamental Properties
๐Ÿค™๐ŸฝUnit 3: Differentiation: Composite, Implicit & Inverse Functions
๐Ÿ‘€Unit 4: Contextual Applications of the Differentiation
โœจUnit 5: Analytical Applications of Differentiation
๐Ÿ”ฅUnit 6: Integration and Accumulation of Change
๐Ÿ’ŽUnit 7: Differential Equations
๐ŸถUnit 8: Applications of Integration
๐Ÿฆ–Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)
FREE AP calc Survival Pack + Cram Chart PDF
Sign up now for instant access to 2 amazing downloads to help you get a 5
Join us on Discord
Thousands of students are studying with us for the AP Calculus AB/BC exam.
join now
๐Ÿ’ช๐Ÿฝ Are you ready for the Calc AB exam?
Take this quiz for a progress check on what youโ€™ve learned this year and get a personalized study plan to grab that 5!
START QUIZ
๐Ÿ’ช๐Ÿฝ Are you ready for the Calc BC exam?
Take this quiz for a progress check on what youโ€™ve learned this year and get a personalized study plan to grab that 5!
START QUIZ
Play this on HyperTyper
Practice your typing skills while reading Ratio Test for Convergence
Start Game
๐Ÿ“ฑ Stressed or struggling and need to talk to someone?
Talk to a trained counselor for free. It's 100% anonymous.
Text FIVEABLE to 741741 to get started.
ยฉ 2021 Fiveable, Inc.