In this video, Patrick teaches how to Differentiate and Integrate Power Series to Derive New Power Series Expressions.

1. Sequence: Convergence and Divergence (Part 1)
2. Sequences: Converging or Diverging (Part 2)
3. Series: Geometric Series and the Test for Divergence
4. Geometric Series: Fraction Representation
5. Examples of Geometric Series and the Test for Divergence (Part 1)
6. Examples of Geometric Series and the Test for Divergence (Part 2)
7. Telescoping Series
8. Series Diverges: Using Partial Sums
9. Integral Test for Series
10. Using the Integral Test for Series: Example 1
11. Using the Integral Test for Series: Example 2
12. Using the Integral Test for Series: Example 3
13. Series: Limit and Direct Comparison Test
14. Series: Limit and Direct Comparison Test Examples
15. Series: Limit and Direct Comparison Test Examples (cont.)
16. Alternating Series (Part 1)
17. Alternating Series (Part 2)
18. Alternating Series Estimation Theorem
19. Ratio Test to Determine if a Series Converges (Ex. 1)
20. Ratio Test to Determine if a Series Converges (Ex. 2)
21. Root Test for Series
22. Power Series Representation of Functions
23. Power Series: Interval of Convergence
24. Differentiating and Integrating Power Series
25. Power Series: Multiplying and Dividing
26. Taylor and MacLaurin Series (Ex. 1)
27. Taylor and MacLaurin Series (Ex. 2)
28. Taylor's Remainder Theorem or Taylor's Inequality
29. The Binomial Series (Ex. 1)
30. The Binomial Series (Ex. 2)

In this course, Calculus Instructor Patrick gives 30 video lessons on Series and Sequences. Some of the Topics covered are: Convergence and Divergence, Geometric Series, Test for Divergence, Telescoping Series, Integral Test, Limit and Direct Comparison Test, Alternating Series, Alternating Series Estimation Theorem, Ratio Test, Power Series, Taylor and MacLaurin Series, Taylor's Remainder Theorem (Taylor's Inequality), Binomial Series, and many more.

Tags: Math Calculus Math