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68-69. Distance traveled by bouncing balls Suppose a ball is thrown upward to a height of ho meters. Each time the ball bounces, it rebounds to a fraction r of its previous height. Let h, be the height after the nth bounce and let Sn be the total distance the ball has trav- eled at the moment of the nth bounce. Find the first four terms of the sequence {Sn}. b. Make a table of 20 terms of the sequence {Sn} and determine a plausible value for the limit of Sn}. 68. ho = 20, r = 0.5 69. ho = 20, r = 0.75

68-69. Distance traveled by bouncing balls Suppose a ball is thrown upward to a height of ho meters. Each time the ball bounces, it rebounds to a fraction r of its previous height. Let h, be the height after the nth bounce and let Sn be the total distance the ball has trav- eled at the moment of the nth bounce. Find the first four terms of the sequence {Sn}. b. Make a table of 20 terms of the sequence {Sn} and determine a plausible value for the limit of Sn}. 68. ho = 20, r = 0.5 69. ho = 20, r = 0.75

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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help with question 69 please?

re- ad hat it Find the Use the results of part (a) to find a formula for Sn. Find the value of the series. ing 20 72. Σ 1.54 A. 63. 2 (2k-1)(2k + 1) 4K² 1 4k² - 1 k=1 64. Further Explorations 67. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. 66. €72/44 23/14 3k The sequence of partial sums for the series 1+ 2+ 3+... is {1, 3, 6, 10, ...}. b. If a sequence of positive numbers converges, then the terms of the sequence must decrease in size. c. If the terms of the sequence {a} are positive and increase in size, then the sequence of partial sums for the series ak diverges. 68-69. Distance traveled by bouncing balls Suppose a ball is thrown upward to a height of ho meters. Each time the ball bounces, it rebounds to a fraction r of its previous height. Let hn be the height eled at the moment of the nth bounce. after the nth bounce and let S, be the total distance the ball has trav- a. Find the first four terms of the sequence {Sn}. plausible value for the limit of {S}. b. Make a table of 20 terms of the sequence {Sn} and determine a 68. ho = 20, r = 0.5 69. ho = 20, r = 0.75 70-77. Sequences of partial sums Consider the following infinite series. a. Write out the first four terms of the sequence of partial sums. b. Estimate the limit of {Sn} or state that it does not exist. 70. Σ cos (πk) 71. 8 Σ9(0.1) k k=1 8 73. Σ 3* k=1 79. Rad othe the whe 80. Co- me the pe CO 81. D a E E 182.
Transcribed Image Text:re- ad hat it Find the Use the results of part (a) to find a formula for Sn. Find the value of the series. ing 20 72. Σ 1.54 A. 63. 2 (2k-1)(2k + 1) 4K² 1 4k² - 1 k=1 64. Further Explorations 67. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. 66. €72/44 23/14 3k The sequence of partial sums for the series 1+ 2+ 3+... is {1, 3, 6, 10, ...}. b. If a sequence of positive numbers converges, then the terms of the sequence must decrease in size. c. If the terms of the sequence {a} are positive and increase in size, then the sequence of partial sums for the series ak diverges. 68-69. Distance traveled by bouncing balls Suppose a ball is thrown upward to a height of ho meters. Each time the ball bounces, it rebounds to a fraction r of its previous height. Let hn be the height eled at the moment of the nth bounce. after the nth bounce and let S, be the total distance the ball has trav- a. Find the first four terms of the sequence {Sn}. plausible value for the limit of {S}. b. Make a table of 20 terms of the sequence {Sn} and determine a 68. ho = 20, r = 0.5 69. ho = 20, r = 0.75 70-77. Sequences of partial sums Consider the following infinite series. a. Write out the first four terms of the sequence of partial sums. b. Estimate the limit of {Sn} or state that it does not exist. 70. Σ cos (πk) 71. 8 Σ9(0.1) k k=1 8 73. Σ 3* k=1 79. Rad othe the whe 80. Co- me the pe CO 81. D a E E 182.
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