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INSTRUCTION
Students might incorrectly state
that a geometric series in which
|r| >1 converges to ∞. Tell
students that geometric series
only converge to a real number
and that ∞ is not considered a
real number.
Example 2 Tie a washer onto
the end of a string to model
the pendulum discussed in this
problem.
Note that in this example, the
pendulum never really stops.
However, the series converges.
Have students discuss why the
pendulum will eventually stop
(friction).
Ongoing Assessment Point
out to students that while terms
of the geometric series alternate
between positive and negative, the
sum of the terms remains positive
and converges towards 5 6 .
a1
S =
1
r
S =
48
1 0.
99
S = 4,
800
1 − 1 1 1
5
+ 25
− 125
+… 5 6
Diversity in the Classroom
Visual Learner
Direct students to a website that provides animated demonstrations of fractal
geometry. Ask students to do additional internet research to compile a list of
five occurrences of fractal geometry in nature.
410 Chapter 9 Sequences and Series