Series Convergence Tests – AP Calculus BC | ShowMeClass

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Series Convergence Tests

AP Calculus BC · Unit 10: Infinite Sequences & Series

Learning Objectives

Apply convergence tests: Ratio, Root, Integral, Comparison, Alternating Series

Distinguish absolutely, conditionally, and divergent series

Visualize partial sums Sₙ and individual terms aₙ

Determine convergence from the behavior of Sₙ

Tests at a Glance

Current Series

SeriesConvergenceAP Calc BCUnit 10

PARTIAL SUMS Sₙ

S_N =—

Converges to—

Verdict—

INDIVIDUAL TERMS aₙ

Series

Number of Terms N 30

Ratio r 0.50

Apply Test

Convergence Analysis

📝 Quick Quiz▼

1. The geometric series Σrⁿ converges when:

|r| < 1 r < 1 r > 0 r ≠ 0

2. The harmonic series Σ1/n:

Converges to 1 Converges to ln(2) Diverges Converges conditionally

3. If lim |aₙ₊₁/aₙ| = L < 1, the Ratio Test says:

Diverges Converges absolutely Inconclusive Converges conditionally