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 $LaTeX: \lbrace r^n\rbrace$ $\lbrace r^n\rbrace$

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 $a_{n}$ $a$ n and $b_{n}$ $b$ n do NOT need to be "strict" - they should technically be $\leq$ $\leq$ and $\geq$ $\geq$ .

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: