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Comparison Tests for Convergence

Hannah Hill

Hannah Hill

6 min read

Study Guide Overview

This guide covers comparison tests for convergence of series in AP Calculus BC. It explains the Direct Comparison Test and the Limit Comparison Test, including conditions for their use. It provides practice examples demonstrating how to apply these tests, using techniques like the p-series test, geometric series test, and L’Hopital’s Rule.

Previous Topic - Harmonic Series and p-SeriesNext Topic - Alternating Series Test for Convergence

Question 1 of 8

🚀 Which of the following series would be most suitable to directly compare with ∑n=1∞1n2+3\sum_{n=1}^{\infty} \frac{1}{n^2 + 3} using the Direct Comparison Test?

∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}

∑n=1∞1n3\sum_{n=1}^{\infty} \frac{1}{n^3}

∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}

∑n=1∞12n\sum_{n=1}^{\infty} \frac{1}{2^n}