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The nth Term Test for Divergence

Next Topic - Integral Test for Convergence
Study Guide Overview

This study guide covers the nth Term Test for Divergence for AP Calculus BC. It explains how to apply the test to determine if a series diverges by evaluating the limit of the nth term as n approaches infinity. It includes a walkthrough example and practice problems with solutions, focusing on converting to limit notation, evaluating the limit, and drawing conclusions based on the test results.

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Previous Topic - Working with Geometric SeriesNext Topic - Integral Test for Convergence

Question 1 of 8

Which of the following correctly states the nth term test for divergence? πŸ€”

If lim⁑nβ†’βˆžan=0\lim_{n \to \infty} a_n = 0limnβ†’βˆžβ€‹an​=0, then the series βˆ‘an\sum a_nβˆ‘an​ diverges

If lim⁑nβ†’βˆžanβ‰ 0\lim_{n \to \infty} a_n \neq 0limnβ†’βˆžβ€‹an​=0, then the series βˆ‘an\sum a_nβˆ‘an​ converges

If lim⁑nβ†’βˆžanβ‰ 0\lim_{n \to \infty} a_n \neq 0limnβ†’βˆžβ€‹an​=0, then the series βˆ‘an\sum a_nβˆ‘an​ diverges

If lim⁑nβ†’βˆžan=0\lim_{n \to \infty} a_n = 0limnβ†’βˆžβ€‹an​=0, then the series βˆ‘an\sum a_nβˆ‘an​ converges