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AP Calculus BC 10.1 Defining Convergent and Divergent Infinite Series Questions

Determine whether an infinite series converges by examining partial sums, identifying familiar forms and checking each test condition.

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

Question 1

[Maximum number: 1]

The infinite series ∑k=1∞ak\sum_{k=1}^{\infty} a_{k} has nth partial sum Sn=n3n+1S_{n}=\frac{n}{3 n+1} for n≥1n \geq 1. What is the sum of the series ∑k=1∞ak\sum_{k=1}^{\infty} a_{k} ?

A

13\frac{1}{3}

B

12\frac{1}{2}

C

1

D

32\frac{3}{2}

E

The series diverges.

Figure for Question 1 — AP Calculus BC
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