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AP Calculus BC 10.9: Absolute & Conditional Convergence

Practise AP Calculus BC 10.9 by testing alternating series and distinguishing absolute convergence, conditional convergence and divergence from the term structure.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • Check whether an alternating series converges while its absolute-value series diverges.
  • Use geometric, p-series and factorial benchmarks to reject absolute or divergent alternatives.

LIM-7.A—Determine whether a series converges or diverges—Topic 10.9 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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