AP®︎ Calculus BC: Topic 10.7 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 10.7 of AP Calculus BC – Alternating Series Test for Convergence.

Questions List

Topic 10.7

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Question 1 Easy

To apply the alternating series test to ∑n=1∞(−1)n+1nn3+2\sum_{n=1}^{\infty}\frac{(-1)^{n+1}n}{n^3+2}, which sequence must be shown to be decreasing with limit 00?

AThe sequence (−1)n+1nn3+2\frac{(-1)^{n+1}n}{n^3+2}
BThe sequence 1n2\frac{1}{n^2}
CThe sequence nn3+2\frac{n}{n^3+2}
DThe partial sums Sn=∑k=1n(−1)k+1kk3+2S_n=\sum_{k=1}^{n}\frac{(-1)^{k+1}k}{k^3+2}

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 10.7: Alternating Series Test for Convergence

Learning Objective: LIM-7.A

Determine whether a series converges or diverges.

Essential Knowledge: LIM-7.A.10

The alternating series test is a method to determine whether an alternating series converges.

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