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AP Calculus BC 10.3 nth-Term Test Overview

Evaluate the limit of the nth term and use a nonzero or nonexistent limit to establish divergence of an infinite series.

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 10.3

10.3 The nth Term Test for Divergence question 1

[Maximum number: 1]

Which series diverges?

A

∑n=1∞(−1)nn5\sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^{5}}

B

∑n=1∞(−1)nn5\sum_{n=1}^{\infty} \frac{(-1)^{n}}{\sqrt[5]{n}}

C

∑n=1∞(−1)n5n+1\sum_{n=1}^{\infty} \frac{(-1)^{n}}{5 n+1}

D

∑n=1∞(−1)n⋅n5n+1\sum_{n=1}^{\infty} \frac{(-1)^{n} \cdot n}{5 n+1}

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