Unit 12: Series

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Essential Questions: 
  • How is it possible to find the sum of an infinite number of terms?
  • What are the advantages of knowing the sum of an infinite series if we can't actually know all the terms?
  • What does infinity really mean if there is a way to add up an infinite number of terms to get a finite answer?
Content: 
  • Geometric connection to series (Fractals)
  • Definition of series.
  • Sigma notation - beginning value, a_n term, number of terms in series
  • Formula for partial sum of an arithmetic series
  • Formula for partial sum of a geometric series
  • Formula for sum of an infinite geometric series - restrictions?
Skills and Processes: 
  • Writing series in sigma notation.
  • Find the a_n term in simple series.
  • Prove the formulas for the sums of a partial arithmetic series, partial geometric series, and an inifinite geometric series.
  • Solving problems using the series formulas.