Testing Convergence at Endpoints

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Section 11.5 – Testing for Convergence at Endpoints.
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Presentation transcript:

Testing Convergence at Endpoints Chapter 10 Infinite Series Section 10.5 Testing Convergence at Endpoints

Quick Review

Quick Review

Quick Review Solutions

Quick Review Solutions

What you’ll learn about The Integral Test Harmonic series and p-series The Limit Comparison Test The Alternating Series Test and Leibniz’s Theorem The strange implication of conditional convergence Finding intervals of convergence Why convergence of a series for f does not imply convergence to f … and why Additional tests for convergence of series are introduced in this section.

The Integral Test

Example Applying the Integral Test

Harmonic Series p-series

The Limit Comparison Test (LCT)

Example Using the Limit Comparison Test

The Alternating Series Test (Leibniz’s Theorem)

The Alternating Series Estimation Theorem

Rearrangement of Absolutely Convergent Series

Rearrangement of Conditionally Convergent Series

How to Test a Power Series for Convergence

Example Finding Intervals of Convergence

Quick Quiz Sections 10.4 and 10.5

Quick Quiz Sections 10.4 and 10.5

Quick Quiz Sections 10.4 and 10.5

Quick Quiz Sections 10.4 and 10.5

Quick Quiz Sections 10.4 and 10.5

Quick Quiz Sections 10.4 and 10.5

Chapter Test

Chapter Test

Chapter Test

Chapter Test

Chapter Test Solutions

Chapter Test Solutions

Chapter Test Solutions

Chapter Test Solutions

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