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AP Calculus BC 10.9 Conditional Series Overview

Classify alternating series by testing convergence with signs retained and after taking absolute values, distinguishing conditional convergence from absolute convergence.

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 10.9

10.9 Determining Absolute or Conditional Convergence question 1

[Maximum number: 1]

11. Which of the following series converges conditionally?

I. ∑n=0∞(−1)n3n2n\sum_{n=0}^{\infty} \frac{(-1)^{n} 3^{n}}{2^{n}}
II. ∑n=1∞(−1)nn3\sum_{n=1}^{\infty} \frac{(-1)^{n}}{\sqrt[3]{n}}
III. ∑n=1∞(−1)nn5\sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^{5}}

A

I only

B

II only

C

I and II only

D

II and III only

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