Session 95: Series Comparison

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Overview

In this session we use Riemann sums to compare series to indefinite integrals. This allows us to determine whether the series converge and may help determine the value of a convergent series.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Comparison of the Harmonic Series (00:08:00)

» Accompanying Notes (PDF)

From Lecture 37 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Comparison Tests (00:04:00)

» Accompanying Notes (PDF)

From Lecture 37 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 3: Examples of Comparison (00:03:00)

» Accompanying Notes (PDF)

From Lecture 37 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

 

Comparison Tests

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Ratio Test for Convergence

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Worked Example

 

Using the Ratio Test

Recitation Video

 

Integral Test for Convergence

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Using the Integral Test for Estimation

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