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12-3
Infinite Geometic Series
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Infinite Geometic Series
A Geometric Series that continues to infinity or negative
infinity
Converges
The terms of a sequence or partial sums of a series
approach a particular value
Limit
the value to which the sequence or sum of a series converges
AN INFINITE GEOMETRIC SERIES CONVERGES
AND THUS HAS A PARTIAL SUM
IF AND ONLY IF
|r|<1
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EXAMPLE 1
Does the series converge?
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Partial Sum Formula
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Example 2
Give the sum of each infinite geometric series.
9+6+4+...
25-5+1-...
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Example 3
Write each infinite geometric series in sigma notation and find
its sum.
16+8+4+...
9-3+1-...
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Example 4
The geometric series 32+24+18+13.5+... represents
lengths, in cm, of swings of a pendulum as it comes to rest.
Find the total distance traveled by the pendulum before
stopping.
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You Try It!
The geometric series 500+400+320+256+... represents the
sum, in feet, a hot air balloon rises each minute. Find the
total altitude gained by the balloon.
HOMEWORK
12-3 worksheet
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