Pre-Cal 40S June 5, 2009

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Infinite geometric sequences.

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Pre-Cal 40S June 5, 2009

  1. 1. Infinite Geometric Series iphone to infinity for righty's by flickr user KIT
  2. 2. Given a geometric sequence in which and , what is the value of ?
  3. 3. Series: The sum of numbers in a sequence to a particular term in a sequence. Example: denotes the sum of the first 5 terms. denotes the sum of the first n terms. Artithmetic Series: The sum of numbers in an arithmetic sequence given by is the sum to the nth term n is the quot;rankquot; of the nth term a is the first term in the sequence d is the common difference
  4. 4. Sigma Notation: A shorthand way to write a series. Example: 4 ∑(2n - 3) means (2(1) -3) + (2(2) -3) + (2(3) -3) + (2(4) -3) n=1 = -1 + 1 + 3 + 5 =8 Σ is capital sigma (from the greek alphabet); means sum subscript n = 1 means quot;start with n = 1 and evaluate (2n - 3)quot; superscript 4 means keep evaluating (2n - 3) for successive integral values of n; stop when n = 4; then add all the terms (2n - 3) is the implicit definition of the sequence
  5. 5. Series: The sum of numbers in a sequence to a particular term in a sequence. Example: denotes the sum of the first 5 terms. denotes the sum of the first n terms. Geometric Series: The sum of numbers in an geometric sequence given by or is the sum to the nth term n is the quot;rankquot; of the nth term a is the first term in the sequence d is the common difference
  6. 6. or
  7. 7. Given the geometric sequence in which and r = , which term has a value of 27? Find the sum of the first 5 terms.
  8. 8. Given the geometric sequence in which and r = , which term has a value of 27? Find the sum of the first 5 terms.
  9. 9. Infinite Geometric Series iphone to infinity for righty's by flickr user KIT
  10. 10. Infinite Geometric Series Why is that the formula?
  11. 11. CONVERGENT SERIES 0 < |r| <1 DIVERGENT SERIES |r| > 1
  12. 12. Find the infinite sum for a geometric series given: a = 12 r= 2 3

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