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AP Calculus BC 10.1: Series Convergence

Practise AP Calculus BC 10.1 by deciding whether infinite series converge, using partial-sum limits and recognising when test conditions are insufficient.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • Use the limit of an nth partial-sum formula to find a series sum or prove divergence.
  • Classify geometric, p-series, factorial and alternating forms as convergent or divergent.

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 LIM-7.A—Determine whether a series converges or diverges question 1 — AP Calculus BC
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