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
» Clip 1: Comparison of the Harmonic Series (00:08:00)
From Lecture 37 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Comparison of the Harmonic Series
> Download from iTunes U (MP4 - 111MB)
> Download from Internet Archive (MP4 - 111MB)
» Clip 3: Examples of Comparison (00:03:00)
From Lecture 37 of 18.01 Single Variable Calculus, Fall 2006
Recitation Video
Comparison Tests
> Download from iTunes U (MP4 - 33MB)
> Download from Internet Archive (MP4 - 33MB)
Ratio Test for Convergence
> Download from iTunes U (MP4 - 30MB)
> Download from Internet Archive (MP4 - 30MB)
Worked Example
Using the Ratio Test
Recitation Video
Integral Test for Convergence
> Download from iTunes U (MP4 - 17MB)
> Download from Internet Archive (MP4 - 17MB)
Using the Integral Test for Estimation
> Download from iTunes U (MP4 - 33MB)
> Download from Internet Archive (MP4 - 33MB)