Unit 7:  Sequence and Series Convergence

Unit 7:  Sequence and Series Convergence

• MonDay 21:  Sequence

  • • Video 1:  What is a Sequence?

    • Video 2:  The Limit of a Sequence

    • Video 3:  Two More Examples

    • Video 4:  Yep... Two More Examples

    • Video 5:  The Monotonic Sequence Theorem

    • Video 6:  Proving Our Sequence is Monotonic

    • Video 7:  Proving Our Sequence is Bounded

    • Video 8:  The Limit of Our Sequence

      • • 8.1:  3-19 odd, 25, 26, 44

          • • • 13 15 25 and 26

• Day 22:  Definition of a Series, Finite Series, Harmonic Series, Test for Divergence, Geometric Series, Telescoping Series

  • • Video 1:  One More Monotonic Sequence

    • Video 2:  The Definition of a Series

    • Video 3:  Finite Series and Summation Notation (French Accents Only Please)

    • Video 4:  Test for Divergence

    • Video 5:  The Flow Chart

      • • Series Flow Chart

    • Video 6:  The Harmonic Series (First Time)

    • Video 7:  Shortcuts Coming

    • Video 8:  An Intoduction to Geometric Series

    • Video 9:  Proof of Geometric Series

    • Video 10: Two Geometric Series Examples

    • Video 11: Telescoping Series

      • • 8.2:  9-27 odd, 33, 35

          • • 23 35

            • These were all shot during the 2019-2020 year when the AP Exam was limited.  These COULD be on the AP Exam this year (ignore when I say they are not on "this year's" test)

            • 11 15 19

            • 20 21 25

• Day 23:  Buffer Day

  • • No New Videos

      • • Be sure to master 8.2 before tomorrow

• Day 24:   Comparison Test, Limit Comparison Test, Integral Test

  • • Video 1:  The Harmonic Series (For a Second Time)

    • Video 2:  What if P = 2?

    • Video 3:  The General Integral Test

    • Video 4:  The P-Series

    • Video 5:  The Flow Chart and the Integral Test

    • Video 6:  The Comparison Test

    • Video 7: The Limit Comparison Test

      • • READ 8.3 and then do 8.3:  7-23 odd q

          • • 12 13 15 19

            • 20 21 23

• FriDay 25:  Integral Test Error, Workday

  • • Video 1:  Estimating The Sum of a Series

      • • Series Estimation Program for TI-Calculators

    • Video 2:  An Error Bound

    • Video 3:  Estimating a Sum

    • Video 4:  Finding N

    • Video 5:  More Practice

    • Video 6:  Last One

      • • 8.3:  26ac, 27ac, 29, 31, 32

          • • 29 most basic level

            • 29 advanced technique book-style.  Read p. 588 - 590

            • 31 32

• MonDay 26:  Alternating Series and Ratio Test, Workday

  • • Video 1:  Alternating Series

    • Video 2:  Couple of Quick Examples

    • Video 3:  Alternating Series Error Bound

    • Video 4:  Absolute Convergence

    • Video 5:  Ratio Test Example 1

    • Video 6:  Ratio Test Example 2

      • • 8.4:  5, 7, 12-14, 17, 19-22

          • • 4 13 14

            • 17 19 20

        • Check CANVAS for Canvas Quiz

• Day 27:  Workday

  • • No New Videos

      • • Buy this AP Prep book to use next semester if you plan to take the AP exam in May

        • If you already did, find the section that reteaches convergence of series, read through it, and attempt some of the practice quizzes

FRQ 14:  Series

(No Calculator)

(You MAY use the flow chart)

(Shoot for about 45 minutes)