The solution of the recurrence relation a n = 4 a n − 1 − 4 a n − 2 + 4 n , n ≥ 2 , with the initial conditions a 0 = 2 , a 1 = 8 by using the method of the characteristic polynomial (as in Section 5.3).

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Answer 1

Question

Chapter 5.4, Problem 8E

(a)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of the characteristic polynomial (as in Section 5.3).

(b)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of generating functions (as in Section 5.3).

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65% of all violent felons in the prison system are repeat offenders. If 43 violent felons are randomly selected, find the probability that a. Exactly 28 of them are repeat offenders. b. At most 28 of them are repeat offenders. c. At least 28 of them are repeat offenders. d. Between 22 and 26 (including 22 and 26) of them are repeat offenders.

Answer 2

Question

Chapter 5.4, Problem 8E

(a)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of the characteristic polynomial (as in Section 5.3).

(b)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of generating functions (as in Section 5.3).

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Answer 3

Question

Chapter 5.4, Problem 8E

(a)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of the characteristic polynomial (as in Section 5.3).

(b)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of generating functions (as in Section 5.3).

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Answer 4

Question

Chapter 5.4, Problem 8E

(a)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of the characteristic polynomial (as in Section 5.3).

(b)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of generating functions (as in Section 5.3).

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Answer 5

Chapter 5.4, Problem 8E

(a)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of the characteristic polynomial (as in Section 5.3).

(b)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of generating functions (as in Section 5.3).

Answer 6

Chapter 5.4, Problem 8E

(a)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of the characteristic polynomial (as in Section 5.3).

Answer 7

Chapter 5.4, Problem 8E

(a)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of the characteristic polynomial (as in Section 5.3).

Answer 8

(b)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of generating functions (as in Section 5.3).

Answer 9

(b)

To determine

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of generating functions (as in Section 5.3).

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 5.1 - True/False Questions The statement i=1n(2i1)=n2...Ch. 5.1 - Prob. 2TFQ Ch. 5.1 - Prob. 3TFQ Ch. 5.1 - Prob. 4TFQ Ch. 5.1 - Prob. 5TFQ Ch. 5.1 - Prob. 6TFQ Ch. 5.1 - Prob. 7TFQ Ch. 5.1 - Prob. 8TFQ Ch. 5.1 - Prob. 9TFQ Ch. 5.1 - Prob. 10TFQ

The solution of the recurrence relation a n = 4 a n − 1 − 4 a n − 2 + 4 n , n ≥ 2 , with the initial conditions a 0 = 2 , a 1 = 8 by using the method of the characteristic polynomial (as in Section 5.3).

Solution Summary: The author explains the method of the characteristic polynomial.

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The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of the characteristic polynomial (as in Section 5.3).

The solution of the recurrence relation an=4an−1−4an−2+4n,n≥2, with the initial conditions a0=2,a1=8 by using the method of generating functions (as in Section 5.3).

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