Pre-Cal 40S Slides June 3, 2008

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Arithmetic and geometric series.

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Pre-Cal 40S Slides June 3, 2008

  1. 1. The Legacy of Karl Fredrich Gauss that is ... unstacking by flickr user mikelietz Zehner by flickr user threedots
  2. 2. Some quot;quickiesquot; to get us started ... Find the value(s) of r in . In the geometric sequence, if = 3 and r = 2 , find . If the first term of a geometric progression is and the common ratio is -3, find the next three terms. Determine the common ratio for the geometric sequence:
  3. 3. http://www.sigmaxi.org/amscionline/gauss-snippets.html The Story of Young Gauss ... Photo Source: Karl Gauss (1777–1855)
  4. 4. 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
  5. 5. Sigma Notation: A shorthand way to write a series. Example: means (2(1) -3) + (2(2) -3) + (2(3) -3) + (2(4) -3) = -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
  6. 6. Introduction to today's class by Mr. Green on YouTube ... a summary of almost everything in this unit ... Sequences and Series on YouTube http://youtube.com/watch?v=WjLSz-nNLBc

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