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Pre-Cal 40S Slides January 18, 2008

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Geometric series.

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Pre-Cal 40S Slides January 18, 2008

1. 1. Listen to the music ... the geometric sequences music .... Intermezzo
2. 2. Evan Ma - Sequences and Series http://youtube.com/watch?v=M1WzkWy3n74
3. 3. The Story of Young Gauss ... Photo Source: Karl Gauss (1777–1855) to be continued ...
4. 4. SEQUENCE SERIES
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. 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
6. 6. (a) What is the sum of the integers from 1 to 5000?
7. 7. (b) What is the sum of all multiples of 7 between 1 & 5000? (c) What is the sum of all integers from 1 to 5000 inclusive that are not multiples of 7?
8. 8. 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
9. 9. Find the value of:
10. 10. Given a geometric sequence in which and , what is the value of ?