Name
Date
Class
Practice B
LESSON
12-5 Mathematical Induction and Infinite Geometric Series
Determine whether each geometric series converges or diverges.
9 __
31…
81 ____
27 ___
1. ____
5
625
125
25
3 ___
9 ____
81 …
27 ____
2. 1 __
5
25
125
625
Diverges
Converges
Find the sum of each infinite geometric series, if it exists.
7 ___
7 …
7 ___
3. 7 __
4
16
64
4. 500 300 180 108 …
28
___
312.5
3
5.
4 3 1 __
4
__
k
6.
k1
99 __94 k
k1
⫺30.46
Does not exist
Write each repeating decimal as a fraction in simplest form.
_
_
_
7. 0.16
8. 0.016
9. 0.016
16
___
16
____
99
_
_
10. 0.045
16
____
999
_
11. 0.1
990
12. 0.123
1
___
1
__
41
____
22
9
333
Identify a counterexample to disprove each statement.
13. 2
n
n
14. n 3n
2
3
Possible answer: n ⫽ ⫺5
Possible answer: n ⫽ ⫺2
Solve.
15. Ron won a prize that pays $200,000 the first year and half of the
previous year’s amount each year for the rest of his life.
a. Write the first 4 terms of a series to represent the situation.
200,000 ⫹ 100,000 ⫹ 50,000 ⫹ 25,000 ⫹ …
b. Write a general rule for a geometric sequence that
models his prize each year.
c. Estimate Ron’s total prize in the first 10 years.
d. If Ron lives forever, what is the total of his winnings?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c12-5_pr.indd 36
36
a n ⫽ 200,000 0.5 n⫺1
$399,609.38
$400,000
Holt Algebra 2
12/29/05 6:46:33 PM
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