ID: 1
MATH 11 - Pre Calculus
UNIT: Series & Sequences
Name___________________________________
Lesson 5 Homework: Infinite Geometric Series
Period____
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Determine whether each infinite geometric series has a finite sum. If so, find the sum.
1) 2 + 3 + 4.5 + 6.75 + ...
3)
1 3
9
27
- +
+ ...
2 8 32 128
2) -0.5 - 0.05 - 0.005 - 0.0005 - ...
4) 0.1 + 0.2 + 0.4 + 0.8 + ...
Write the first 4 terms of each infinite geometric series.
5) t1 = 4 and r =
1
5
6) t1 =
3
3
and r = −
2
8
Determine the sum of each of the infinite geometric series.
7) 8 + 2 + 0.5 + 0.125 + ...
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8) -1 -
-1-
3 9 27
- ...
4 16 64
Worksheet by Kuta Software LLC
9) 10 -
20 40 80
+
+ ...
3
9 27
10) -2 +
2 2
2
- +
- ...
3 9 27
Write a sentence to answer each question.
11) By looking at the common ratio, how do we
know that the series is convergent?
12) By looking at the common ratio, how do we
know that the series is divergent?
Find the indicated value.
13) t1 = 21 and S ∞ = 63 ; Find r
14) r =
3
24
and S ∞ =
4
7
Use an infinite geometric series to express each repeating decimal as a fraction.
15) 0.4979797...
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16) 1.143143143...
-2-
Worksheet by Kuta Software LLC
ID: 1
MATH 11 - Pre Calculus
UNIT: Series & Sequences
Name___________________________________
Lesson 5 Homework: Infinite Geometric Series
Period____
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Determine whether each infinite geometric series has a finite sum. If so, find the sum.
1) 2 + 3 + 4.5 + 6.75 + ...
2) -0.5 - 0.05 - 0.005 - 0.0005 - ... Yes. r =
1
so the series con
10
No. r = 1.5 so series diverges.
3)
1 3
9
27
- +
+ ...
2 8 32 128
Yes. r =
4) 0.1 + 0.2 + 0.4 + 0.8 + ...
No. r = 2
3
so the series converges. S ∞ = 2
4
Write the first 4 terms of each infinite geometric series.
5) t1 = 4 and r =
4+
1
5
6) t1 =
3
3 3 9
27
81
and r = −
+
2
8 2 16 128 1024
4
4
4
+
+
5 25 125
Determine the sum of each of the infinite geometric series.
7) 8 + 2 + 0.5 + 0.125 + ...
8) -1 -
32
or 10.666...
3
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3 9 27
- ...
4 16 64
-4
-1-
Worksheet by Kuta Software LLC
9) 10 -
20 40 80
+
+ ...
3
9 27
10) -2 +
2 2
2
3
- +
- ... − or -1.5
3 9 27
2
6
Write a sentence to answer each question.
11) By looking at the common ratio, how do we
know that the series is convergent?
12) By looking at the common ratio, how do we
know that the series is divergent?
The common ratio is smaller than -1 and greater than 1
The common ratio is greater than -1 and less than 1
Find the indicated value.
13) t1 = 21 and S ∞ = 63 ; Find r
r=
3
24
and S ∞ =
4
7
t1 = 6
14) r =
2
3
Use an infinite geometric series to express each repeating decimal as a fraction.
493
1142
15) 0.4979797...
16) 1.143143143...
990
999
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-2-
Worksheet by Kuta Software LLC