# Calculus with Dr. Bob VI: Sequences and Series

### Course Description

In this series, Dr. Bob covers topics from Calculus II on the subject of sequences and series, in particular the various methods (tests) to determine if convergence exists.

Topics include: Sequences, Infinite Series, Integral Test, Comparison Tests, Alternating Series, Ratio Test, Root Test, Power Series, Maclaurin and Taylor Series, and much more.

Dr. Bob in Lesson 14: The Integral Test for Series 1a - Definition/ Examples
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### Video Lectures & Study Materials

# Lecture Play Lecture
1 Sequences: Definitions, Squeeze Theorem Play Video
2 Examples of Sequences Play Video
3 Examples of Recursive Sequences Play Video
4 Sequences 1b - Squeeze Theorem/ Monotone Convergence Theorem Play Video
5 Sequences 2 - Examples of Convergent/Monotonic/Bounded Play Video
6 Sequences 3 - Limit of sqrt(n^2 + n) - n Play Video
7 Sequences 4 - Example of Monotone Convergence Theorem Play Video
8 Infinite Series 1a - Definitions Play Video
9 Infinite Series 1b - Geometric Series/ Limit Test for Divergence Play Video
10 Infinite Series 1c - Telescoping Series Play Video
11 Infinite Series 2 - Example of Convergence/Divergence Play Video
12 Infinite Series 3 - Decimal Expansion of Fractions Play Video
13 Fractals Play Video
14 The Integral Test for Series 1a - Definition/ Examples Play Video
15 The Integral Test for Series 1b - More Examples/ p-Series Play Video
16 The Integral Test for Series 2 - More Examples Play Video
17 Estimating Sums with the Integral Test Play Video
18 Direct Comparison Test for Series 1 Play Video
19 Divergence of Series for 1/ln(n) Play Video
20 Limit Comparison Test for Series 1 Play Video
21 Limit Comparison Test for Series 2 Play Video
22 Rational Function Test for Series Play Video
23 Alternating Series 1a - Alternating Series Test Play Video
24 Alternating Series 1b - Estimating the Remainder Play Video
25 Alternating Series 1c - More Remainder Estimates Play Video
26 Absolute Convergence Test Play Video
27 The Ratio Test for Series Play Video
28 Series Convergence for n!/n^n Play Video
29 The Root Test for Series Play Video
30 Root Test for Series Sum (1-1/n^2)^{n^3} Play Video
31 Series Test Round-Up 1 Play Video
32 Series Test Round-Up 2 Play Video
33 Series Test Round-Up 3 Play Video
34 Motivating Taylor Polynomials 1 Play Video
35 Motivating Taylor Polynomials 2 Play Video
36 Application of Taylor Series: Re-centering Polynomials Play Video
37 Approximating with Maclaurin Polynomials Play Video
38 Approximating with Taylor Polynomials Play Video
39 Fast Maclaurin Polynomial for Rational Function Play Video
40 Taylor's Theorem for Remainders Play Video
41 Taylor's Theorem : Remainder for 1/(1-x) Play Video
42 Power Series 1a - Interval and Radius of Convergence Play Video
43 Power Series 1b - Interval of Convergence Using Ratio Test Play Video
44 Example of Interval of Convergence Using Ratio Test Play Video
45 Power Series 1c - Interval of Convergence Using Root Test Play Video
46 Power Series 1d - Finding the Center Play Video
47 Power Series with Squares Play Video
48 Derivative/Antiderivative of a Power Series 1a - Basics Play Video
49 Derivative/Antiderivative of a Power Series 1b - Interval of Convergence Play Video
50 Derivative/Antiderivative of a Power Series 1c - More Examples Play Video
51 Increasing the Interval of Convergence Play Video
52 Constructing Power Series from Functions 1a - Geometric Power Series Play Video
53 Constructing Power Series from Functions 1b - More Geometric Power Series Play Video
54 Constructing Power Series from Functions 1c - Taylor Coefficients Play Video
55 The Taylor Series for f(x) = ln(x) at x = 1 Play Video
56 The Maclaurin Series for f(x) = 1/(1-x)^2 Play Video
57 The Maclaurin Series for f(x) = e^x Play Video
58 The Maclaurin Series for sin(x), cos(x), and tan(x) Play Video
59 The Maclaurin Series of f(x) = (1+x)^{1/2} 1a Play Video
60 The Maclaurin Series for f(x) = (1+x)^{1/2} 1b Play Video

Displaying 1 comment:

Leckson Mukavhi wrote 3 years ago. - Delete
The videos are great and fascinating. I wish to use them for
my mathematics laboratory teaching and learning as part of
my PhD thesis quasi-experimental
design methodology. Are any written authorizing document
for access and use?

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