AP®︎ Calculus BC: Topic 10.5 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 10.5 of AP Calculus BC – Harmonic Series and p-Series.


Questions List

Topic 10.5

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Q14

Question 1 Easy

Which of the following statements about the series 1+12+13+14+⋯1+\frac12+\frac13+\frac14+\cdots, including its reason, is correct?

AThe series converges, because its terms approach 00.
BThe series converges, because it is a p-series with p=1p=1.
CThe series diverges, because it is the harmonic series ∑n=1∞1n\sum_{n=1}^{\infty}\frac1n.
DThe series diverges, because its terms approach 00.

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 10.5: Harmonic Series and p -Series

Learning Objective: LIM-7.A

Determine whether a series converges or diverges.

Essential Knowledge: LIM-7.A.7

In addition to geometric series, common series of numbers include the harmonic series, the alternating harmonic series, and p -series.