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Today’s Objectives :

Precalculus 2. Today’s Agenda. Today’s Objectives :. Identify divergent and convergent series Find the sum of a infinite geometric series. Do Now . Notes: Convergent & Divergent Series. Work Time . 4. Summary. DUE TODAY: HW #33 Page 661 #23-28 Page 659 #6 Page 660 #15-22

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Today’s Objectives :

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  1. Precalculus 2 Today’s Agenda Today’s Objectives: • Identify divergent and convergent series • Find the sum of a infinite geometric series • Do Now • Notes: • Convergent & Divergent Series • Work Time • 4. Summary • DUE TODAY: HW #33 • Page 661 #23-28 • Page 659 #6 • Page 660 #15-22 • Due TOMORROW: HW #34 • Page 661 #29 – 36

  2. Infinite Geometric Series What do you think about the nth partial sum of a geometric series with a common ratio greater than one? then the terms of the series do not approach zero DIVERGENT series What do you think about the nth partial sum of a geometric series with a common ratio less than one? then the terms of the series approach zero and the geometric series converges to a limit CONVERGENT series

  3. Sum of a Convergent Geometric Series Because the amount being added becomes smaller and smaller, eventually you’re adding next to nothing, so there is a limit to what the sum can be. We can express this with the equation:

  4. Try an example: To what limit does the geometric series 50 + 45 + 40.5 + … converge?

  5. Try an example: To what limit does the geometric series 50 + 45 + 40.5 + … converge?

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