Calculus: The Direct Comparison Test is used to show the divergence of the series sum 1/ln(n).

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

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.