Warm-up: Evaluate
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11.4 Infinite Geometric Series
* a geometric series that does not end
Consider the infinite geometric series below:
You have learned that
n terms of a series.
For an infinite series,
is the sum of the first
is a partial sum.
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In the table below, what is
approaching?
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Formula for the sum of an
Infinite Geometric Series
We will derive the infinite geometric series
formula using the sum of a finite geometric
series:
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Sum of an infinite geometric series:
for which
For
, the sum does not exist because
as n increases,
rapidly increases and has
no limit.
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Convergent and Divergent Series
A series that has a sum is a convergent series,
because its sum converges to a specific value.
A series that does not have a sum is a
divergent series.
Example 1: Determine whether each infinite geometric
series is convergent or divergent.
a.
b.
c.
d.
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Example 2: Find the sum of each infinite geometric series,
if it exists. Also, determine whether each
infinite geometric series converges or diverges.
a.
b.
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Your turn: Find the sum of each infinite geometric series,
if it exists. Also, determine whether each
infinite geometric series converges or diverges.
a.
b.
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Example 3: Evaluate the following.
a.
b.
c.
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