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Alternating Series Test for Convergence

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Study Guide Overview

This study guide covers the Alternating Series Test for convergence in AP Calculus BC. It explains the theorem, which states conditions for convergence (limit of an = 0 and an decreases). It provides a breakdown of the theorem with the alternating harmonic sequence as an example and includes practice problems and solutions for applying the alternating series test.

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Question 1 of 10

What are the two conditions that must be met for an alternating series ∑(−1)nan\sum (-1)^n a_n∑(−1)nan​ to converge according to the Alternating Series Test? 🤔

  1. lim⁡n→∞an=1\lim_{n\to \infty} a_n = 1limn→∞​an​=1 and 2. ana_nan​ is increasing
  1. lim⁡n→∞an=0\lim_{n\to \infty} a_n = 0limn→∞​an​=0 and 2. ana_nan​ is decreasing
  1. lim⁡n→∞an=∞\lim_{n\to \infty} a_n = \inftylimn→∞​an​=∞ and 2. ana_nan​ is decreasing
  1. lim⁡n→∞an=0\lim_{n\to \infty} a_n = 0limn→∞​an​=0 and 2. ana_nan​ is increasing