Calculus Videos: Series and Sequences

Video Lectures

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