*Section 11-5 Geometric Series
Monday, May 13, 2013
12:41 PM
Geometric Series
A geometric series is the expression for the sum of the terms of a geometric
sequence.
Sum of a Finite Geometric Series
The sum, S of a finite geometric series a + a + a + . . . + a , r=1 , is
where a is the first term, r is the common ratio, and n is the number terms.
Ex. 1 Use the formula to evaluate the series: 5 + 15 + 45 + 135 + 405 + 1215.
Evaluating Infinite Geometric Series
There are two types of Infinite Geometric Series:
1. Converging Infinite Series - |r|<1. The series gets closer and closer to
the sum, S. The values of the terms become smaller.
2. Diverging Infinite Series - |r|>1. The series approaches no limit. The
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values of the terms keep getting bigger.
Ex. 2 Decide whether each infinite geometric series diverges or converges. State
whether the series has a sum.
a)
b) 2 + 6 + 18 + . . .
For the Geometric Infinite Series that Converge, use the following formula to
evaluate.
Sum of an Infinite Geometric Series
An infinite geometric series with |r|< 1 converges to the sum
Where a is the first term and r is the common ratio.
Ex. 3 Evaluate the infinite geometric series 120 + 96 + 76.8 + 61.44 + . . .
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Ex. 4 Evaluate each infinite series that has a sum.
a)
b)
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