Intro to Infinite Series Geometric Series

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Intro to Infinite SeriesGeometric Series

• Lesson 8.2

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Definition of Series

• Consider summing the terms of an infinite
  sequence
• We often look at a partial sum of n terms

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Definition of Series

• We can also look at a sequence of partial sums
  Sn
• The series can converge with sum S
• The sequence of partial sums converges
• If the sequence Sn does not converge, the
  series diverges and has no sum

ViewSpreadsheetExample
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Examples

• Convergent
• Divergent

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Telescoping Series

• Consider the series
• Represent as partial fraction
• Expand
• Regroup
• Telescope and evaluate

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Properties of Infinite Series

• Linearity
• The series of a sum the sum of the series
• Use the property

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Geometric Series
ViewSpreadsheetExample (Again)

• Definition
• An infinite series
• The ratio of successive terms in the series is a
  constant
• Example
• What is r ?

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Geometric Series Theorem

• Given geometric series(with a ? 0)
• Series will
• Diverge when r 1
• Converge when r lt 1
• Examples
• Compound interest

Or
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Assignment A

• Lesson 8.2A
• Page 511
• Exercises 5 29 odd

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Apply to Repeating Decimals

• Given repeating decimal
• Consider this as repeating part of the decimal is
  a geometric series
• What is the a? The r ?

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Apply to Repeating Decimals

• Rewrite
• Apply formula for sum of geometric series
• Combine

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Applications

• A pendulum is released throughan arc of length
  20 cmfrom vertical
• Allowed to swing freelyuntil stop, each swing
  90as far as preceding
• How far will it traveluntil it comes to rest?

20 cm
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Assignment B

• Lesson 8.2B
• Page 512
• Exercises 31, 33, 35, 47 55 odd