Geometric Series

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Section 8.4

• Geometric Series

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Geometric Series

• The sum of a geometric sequence

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Theorem

• The sum Sn g1 g2 gn where g1 1st term
  and has a constant ratio r?1 is

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Example 1

• Evaluate

Would each term form a geometric sequence?
S6 32.881
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Example 2

• In a set of 10 dolls, each is 5/6 the height of
  the taller one. If the first doll is 15cm, what
  is the total height of the dolls?

75.5 cm
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Example 3

• 2 children marry and each of them has 2 children.
  Each of them marry and has 2 children, and so
  on. In how many generations will you have 1000
  descendants?

-500 1 - 2n
501 2n
log 501 log 2n
n 9
9 generations
1000 -2(1-2n)