Explanation Given that { a r } is the number of ways of buying r batteries from the store that has 3 C batteries, 4 D batteries, and 6 AA batteries. Also, the AA batteries are sold in a set of two. Here, 0 through 3 batteries of C has to be brought, 0 through 4 batteries of D has to be brought and 0 through 6 batteries of AA has to brought for a total of r batteries. It is appropriate that this is a polynomial of degree 13, because the total batteries to be brought is 13. Since AA batteries are sold in a set of two, buying a battery from the 6AA batteries determines whether to buy 0AA battery, 2AA battery, 4AA battery, etc. Clearly, a r = 0 for r > 13 . Thus, the required polynomial is evaluated as follows. The first polynomial below represents the generating function for 3C batteries, the second one represents the function for 4D batteries and so on. ( 1 + x + x 2 + x 3 ) ( 1 + x + x 2 + x 3 + x 4 ) ( 1 + x 2 + x 4 + x 6 ) = 1 ( 1 + x + x 2 + x 3 + x 4 ) ( 1 + x 2 + x 4 + x 6 ) + x ( 1 + x + x 2 + x 3

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ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 9.5, Problem 16E

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To evaluate: The generating function for the sequence {ar} and to write it in the form a0+a1x+a2x2+a3x3+⋯+a6x6.

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Chapter 9.5, Problem 15E

Chapter 9.5, Problem 17E

Chapter 9 Solutions

Discrete Mathematics

Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Suppose that you have an unlimited supply of red,...Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.2 - Prove by mathematical induction that n2 − n + 2 is...Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prove by mathematical induction that is a...Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - Prob. 12E Ch. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - 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The generating function for the sequence { a r } and to write it in the form a 0 + a 1 x + a 2 x 2 + a 3 x 3 + ⋯ + a 6 x 6 .

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To evaluate: The generating function for the sequence {ar} and to write it in the form a0+a1x+a2x2+a3x3+⋯+a6x6.

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Chapter 9 Solutions