Explanation Given that { a r } is the number of ways of spending r dollars on posters, that is 4 identical $1 posters and 3 identical $2 posters. Here, 0 through 4 posters of $1, 0 through 3 posters of $2 are available for a total of r dollars. It is appropriate that this is a polynomial of degree 10, because the total posters are available for $10. Since 3 identical $2 posters are available, spending a dollar determines whether to spend $0, $2, $4, etc. Clearly, a r = 0 for r > 10 . Thus, the required polynomial is evaluated as follows. The first polynomial below represents the generating function for 4 posters of $1, the second one represents the function for 3 posters of $2. ( 1 + x + x 2 + x 3 + x 4 ) ( 1 + x 2 + x 4 + x 6 ) = 1 ( 1 + x 2 + x 4 + x 6 ) + x ( 1 + x 2 + x 4 + x 6

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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 18E

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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 17E

Chapter 9.5, Problem 19E

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Chapter 9 Solutions

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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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Chapter 9 Solutions