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Pre-Cal 40S Slides May 30, 2007

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The story of Young Gauss. Arithmetic and geometric series.

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Pre-Cal 40S Slides May 30, 2007

1. 1. 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:
2. 2. The Story of Young Gauss ... Photo Source: Karl Gauss (1777–1855)
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: 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