List of Videos in the ISM

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1. Introduction to Infinite Sequences and Series
   1. Videos on Infinite Sequences
   • Patrick JMT: What is a Sequence? Basic Sequence Info
   • Patrick JMT: Sequences – Examples Showing Convergence or Divergence
   • Math Is Power 4U: Limits of a Sequence
   • Math Is Power 4U: Limits of a Sequence: The Squeeze Theorem
   2. Videos on Sigma Notation
   • Patrick JMT: What is a Series?
   • Math Is Power 4U: Introduction to Infinite Series
   3. Introduction to Infinite Series Videos
      • Kahn Academy: Sequences and Series Part II
      • Kahn Academy: Series Sum Example
      • Patrick JMT: Geometric Series: Expressing a Decimal as a Rational Number
      • Math Is Power 4U: Infinite Geometric Series
      • UBC Mathematics Department: Geometric Interpretation of the Geometric Series
   4. Properties of Convergent Infinite Series
   5. Videos on Telescoping and Harmonic Series
   • MIT Opencourseware: Limit of a Series
   • Patrick JMT: Showing a Series Diverges Using its Partial Sums
2. Convergence Tests for Infinite Series
   1. Videos on The Divergence Test
   • Patrick JMT: Showing a Series Diverges Using its Partial Sums
   • Patrick JMT: Geometric Series and the Test for Divergence (Part 1)
   • Patrick JMT: Geometric Series and the Test for Divergence (Part 2)
   2. Videos on The Integral Test
   • Math Is Power 4U: The Integral Test
   • Math Is Power 4U: The p-Series Test
   • Patrick JMT: Using the Integral Test for Series
   3. Alternating Series Test Videos
   • Math Is Power 4U: The Alternating Series Test
   • Patrick JMT: Alternating Series
   • Patrick JMT: More Alternating Series Examples
   4. Videos on The Ratio Test
   • Patrick JMT: Using the Ratio Test to Determine if a Series Converges #1
   • Patrick JMT: Using the Ratio Test to Determine if a Series Converges #2
   5. Review of Convergence Test Videos
   • Patrick JMT: Convergence Test Videos
3. Power Series
   1. Power Series
   • MIT Opencourseware: Ratio Test – Radius of Convergence
   • Math Is Power 4U: Power Series – Part 1
   • Math Is Power 4U: Power Series – Part 2
   2. Taylor and MacLaurin Series
   • Maclaurin Expansion of e^x
   • Kahn Academy: Visualizing Taylor Series for e^x
   • Maclaurin Expansion of sin(x)
   • Kahn Academy: Sine Taylor Series at 0
   • Maclaurin Expansion of cos(x)
   • Kahn Academy: Cosine Taylor Series at 0
   • Videos on Taylor Series
   • MIT Opencourseware: Finding Taylor’s Series
   • MIT Opencourseware: Taylor’s Series of a Polynomial

Previous: Proof of the Ratio Test

Next: Download