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AP Calculus BC 10.5 Harmonic Series & p-Series

Practise AP Calculus BC 10.5 by comparing harmonic and p-series benchmarks, recognising term behaviour, and deciding whether an infinite series converges or diverges.

Syllabus
Effective Fall 2020
Course
AP Calculus BC

Exam points

  • Compare each general term with harmonic and p-series benchmarks to identify convergence or divergence.

LIM-7.A—Determine whether a series converges or diverges—Topic 10.5 question 1

[Maximum number: 1]

24. Which one of the following series converges?

A

∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}

B

∑n=1∞12n+1\sum_{n=1}^{\infty} \frac{1}{2 n+1}

C

∑n=1∞nn2+1\sum_{n=1}^{\infty} \frac{n}{n^{2}+1}

D

∑n=1∞1n2+1\sum_{n=1}^{\infty} \frac{1}{n^{2}+1}

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