Determining Absolute or Conditional Convergence

Benjamin Wright

5 min read

Next Topic - Alternating Series Error Bound

Study Guide Overview

This study guide covers absolute and conditional convergence for AP Calculus BC. It explains the difference between these two types of convergence, provides examples of how to determine each, and uses tests like the alternating series test and direct comparison test. It also emphasizes specifying conditional convergence clearly.

#10.9 Determining Absolute or Conditional Convergence

Welcome to the ninth topic in the final unit! In this topic, we’ll talk about the different types of convergence you can have and how to determine if something is absolutely convergent, conditionally convergent, or divergent! ✨

#📈 Different Types of Convergence

There are two types of convergence that you’ll go over in AP Calculus BC: absolute convergence and conditional convergence.

#💭 Absolute vs. Conditional Convergence

A series $\sum a_n$ is called absolutely convergent if and only if the absolute value of $a_n$ is convergent. If $\sum a_n$ is convergent but $\sum |a_n|$ is divergent, then the series is considered conditionally convergent.

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Question 1 of 11

A series $\sum a_n$ is absolutely convergent if and only if:

$\sum a_n$ converges

$\sum |a_n|$ converges

$\sum a_n$ diverges

$\sum |a_n|$ diverges