# Calculus Videos: Series and Sequences

## Video Lectures

Displaying all 30 video lectures.
 Lecture 1 Play Video Sequence: Convergence and Divergence (Part 1) Lecture 2 Play Video Sequences: Converging or Diverging (Part 2) Lecture 3 Play Video Series: Geometric Series and the Test for Divergence Lecture 4 Play Video Geometric Series: Fraction Representation In this video lesson, Patrck teaches how to find the Fraction Representation of a Rational Number Written as a Decimal. Lecture 5 Play Video Examples of Geometric Series and the Test for Divergence (Part 1) Lecture 6 Play Video Examples of Geometric Series and the Test for Divergence (Part 2) Lecture 7 Play Video Telescoping Series Lecture 8 Play Video Series Diverges: Using Partial Sums Lecture 9 Play Video Integral Test for Series Lecture 10 Play Video Using the Integral Test for Series: Example 1 Lecture 11 Play Video Using the Integral Test for Series: Example 2 Lecture 12 Play Video Using the Integral Test for Series: Example 3 Lecture 13 Play Video Series: Limit and Direct Comparison Test Lecture 14 Play Video Series: Limit and Direct Comparison Test Examples Lecture 15 Play Video Series: Limit and Direct Comparison Test Examples (cont.) Lecture 16 Play Video Alternating Series (Part 1) Lecture 17 Play Video Alternating Series (Part 2) Lecture 18 Play Video Alternating Series Estimation Theorem Lecture 19 Play Video Ratio Test to Determine if a Series Converges (Ex. 1) Lecture 20 Play Video Ratio Test to Determine if a Series Converges (Ex. 2) Lecture 21 Play Video Root Test for Series Lecture 22 Play Video Power Series Representation of Functions In this video, Patrick manipulates the Power Series Representation of 1/(1-x) to derive Power Series Representations of other Functions. Lecture 22 Play Video Power Series: Interval of Convergence Lecture 23 Play Video Differentiating and Integrating Power Series In this video, Patrick teaches how to Differentiate and Integrate Power Series to Derive New Power Series Expressions. Lecture 24 Play Video Power Series: Multiplying and Dividing Lecture 25 Play Video Taylor and MacLaurin Series (Ex. 1) Lecture 26 Play Video Taylor and MacLaurin Series (Ex. 2) Lecture 27 Play Video Taylor's Remainder Theorem or Taylor's Inequality Lecture 28 Play Video The Binomial Series (Ex. 1) Lecture 29 Play Video The Binomial Series (Ex. 2) In this video lesson, Patrick shows how to use Binomial Series to find a Maclaurin series representation for arcsin(x). * There is a small mistake at the end: The power should be (2n+1).