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 LaTeX: \lbrace r^n\rbrace{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   n and  bnbn bb   n do NOT need to be "strict" - they should technically be    and   .


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: