13 3 arithmetic and geometric series and their sums

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13 3 arithmetic and geometric series and their sums

  1. 1. Objectives: 1. Find the sum of the first n terms of arithmetic or geometric series
  2. 2. What is a Series? The sum of the terms of a sequence. Finite sequence: 2, 6, 10, 14 Finite series: 2 + 6 + 10 + 14 Infinite sequence: Infinite series:
  3. 3. Notation Sn represents the sum of n terms of a series. Explicit definition of Sn Sn = t1 + t2 + t3 + … + tn
  4. 4. Finite Arithmetic Series The sum of the first n terms of an arithmetic series is: (The number of terms times the avg. of the first and last terms.)
  5. 5. Example 1 Find the sum of the cubes of the first 20 positive integers.
  6. 6. Example 2 Find the sum of the first 25 terms of the series 11 + 14 + 17 + 20 + …
  7. 7. You Try! Find the sum of the series: 3 + 7 + 11 + … + 99
  8. 8. Finite Geometric Series The sum of the first n terms of a geometric series is:
  9. 9. Example Find the sum of the first 10 terms of 2 – 6 + 18 – 54 + ….
  10. 10. You Try! Find the sum of 3 + 9 + 27 + … + 6561

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