Math 20B: Chapter 11, Infinite Sequences and Series - Videos
By Tracie Catania
Section 11.1: Infinite Sequences
Introductory video with strategies for finding limits. NOTE: there's an error at about the 8 minute mark and I don't want to re-record the whole video! The last term listed in the Fibonacci sequence is incorrect. It should be 21, not 22. Sorry!
Sequences of the form {rn}
Definitions: increasing, decreasing, monotonic, bounded... plus a theorem and an example!
Section 11.2: Infinite Series
Introduction to infinite series
Geometric series - explanation, theory, and an example
Telescoping series: one example
Section 11.3: The Integral Test
Introduction to the Integral Test, "p-series", and one challenging example
This video explains WHY the integral test works
Section 11.4: The Comparison Tests
Introduction to the DIRECT comparison test. Note: the inequalities involving anan aa
Introduction to the LIMIT comparison test
This video shows how to sneaky direct comparison problem involving n!.
Section 11.5: The Alternating Series Test
Introduction to the AST
Section 11.6: Absolute Convergence, Ratio, and Root Tests
Absolute and Conditional Convergence definitions and examples
Absolute Convergence Test
Ratio Test Introduction
Ratio Test example (Stewart ET 11.6 #21)
Root Test Introduction
Section 11.7: Strategy for Testing Series
Here's my Series Summary Sheet with all of the "tests" from 11.2 through 11.6
Section 11.8: Power Series
Introduction to Power Series
Desmos graph for geometric series (Links to an external site.) in the video above
Example: finding the Radius and Interval of Convergence:
Section 11.9: Representations of Functions as Power Series
Introduction:
Section 11.10: Taylor and Maclaurin Series
Introduction to Taylor and Maclaurin Series:
Here's the link to the Desmos graph for the Maclaurin series for the exponential function.
Here's a challenging Taylor Series problem with the square root function:
Section 11.11: Applications of Taylor Polynomials
Inroduction: