Explanation Given: The recurrence relation of a n Formulas used: a n − 1 = a n − ∇ a n Proof: A recurrence relation is an equation consist of a sequence in which the next term is a function of the previous terms. Let us assume the recurrence relation is a n = F 1 a n − 1 + F 2 a n − 2 + F 3 a n − 3 + ......... We know that difference equation a n − 1 = a n − ∇ a n ⇒ a n − 2 = a ( n − 1 ) − 1 = a n − 1 − ∇ a n − 1 = a n − 2 ∇ a n + ∇ 2 a n ⇒ a n − 2 = a n − 2 ∇ a n + ∇ 2 a n ⇒ a n − 3 = a ( n − 2 ) − 1 = a n − 3 ∇ a n + 3 ∇ 2 a n − ∇ 3 a n And then so on…. Then, the recurrence relation becomes, a n = F 1 a n − 1 + F 2 a n − 2 + F 3 a n − 3 +

Discrete Mathematics And Its Applications 7th Edition

7th Edition

ISBN: 9781259152153

Author: Kenneth H. Rosen

Publisher: MCG CUSTOM

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Chapter 8.1, Problem 52E

To determine

To prove:

That the recurrence relation for an can be written as difference equation that is in terms of an,∇an,∇2an.

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Chapter 8.1, Problem 51E

Chapter 8.1, Problem 53E

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Chapter 8 Solutions

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To prove: That the recurrence relation for a n can be written as difference equation that is in terms of a n , ∇ a n , ∇ 2 a n .

Solution Summary: The author explains that the recurrence relation for a_n can be written as difference equation.

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To prove:

That the recurrence relation for an can be written as difference equation that is in terms of an,∇an,∇2an.

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Chapter 8 Solutions

To prove: That the recurrence relation for a n can be written as difference equation that is in terms of a n , ∇ a n , ∇ 2 a n .

Solution Summary: The author explains that the recurrence relation for a_n can be written as difference equation.

Concept explainers

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To prove: That the recurrence relation for an can be written as difference equation that is in terms of an,∇an,∇2an.

Want to see the full answer?

Chapter 8 Solutions

To prove:

That the recurrence relation for an can be written as difference equation that is in terms of an,∇an,∇2an.