AP®︎ Calculus BC: Topic 10.8 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 10.8 of AP Calculus BC – Ratio Test for Convergence.

Questions List

Topic 10.8

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Question 1 Easy

For the series ∑n=1∞an\sum_{n=1}^{\infty} a_n, an>0a_n>0 for all nn and lim⁡n→∞an+1an=34\displaystyle\lim_{n\to\infty}\frac{a_{n+1}}{a_n}=\frac34. Which of the following must be true?

AThe series converges, and its sum is 34\frac34.
BThe series diverges, because its terms approach 34\frac34.
CThe series converges, and lim⁡n→∞an=0\displaystyle\lim_{n\to\infty}a_n=0.
DNo conclusion about convergence can be drawn without a formula for ana_n.

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Calculus BC Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 10.8: Ratio Test for Convergence

Learning Objective: LIM-7.A

Determine whether a series converges or diverges.

Essential Knowledge: LIM-7.A.11

The ratio test is a method to determine whether a series of numbers converges or diverges. Exclusion: The nth term test for divergence, and the integral test, comparison test, limit comparison test, alternating series test, and ratio test for convergence are assessed on the AP Calculus BC Exam. Other methods are not assessed on the exam. However, teachers may include additional methods in the course, if time permits.

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