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AP Calculus BC 10.5 Harmonic Series and P Series Questions

Recognize harmonic and p-series forms, apply the exponent criterion and connect them to convergence comparisons when a direct test is not sufficient.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • identify the governing calculus relationship in the problem
  • justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

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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