Explanation Given: The values are a 0 = 1 a n d b 0 = 2 Formulae used: Recurrence relation and iteration. Calculation: Let us consider the following system of recurrence relations a n = a n − 1 + b n − 1 b n = a n − 1 − b n − 1 w i t h a 0 = 1 a n d b 0 = 2 We add the following equations, a n = a n − 1 + b n − 1 ..................... ( 1 ) b n = a n − 1 − b n − 1 ..................... ( 2 ) − − − − − − − − − − − − − − − − − a n + b n = 2 a n − 1 b n = 2 a n − 1 − a n ....................... ( 3 ) We substitute the value in the equation (1), a n = a n − 1 + 2 a n − 2 − a n − 1 a n = 2 a n − 2 Therefore, by using iteration, a 2 n = 2 a 2 n − 2 = 2 ( 2 a 2 n − 4 ) = 2 2 ( 2 a 2 n − 6 ) .

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ISBN: 9781264309696

Author: ROSEN

Publisher: MCG

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Chapter 8, Problem 8SE

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To calculate:

The solution of the simultaneous system of recurrence relations

an=an−1+bn−1 and bn=an−1−bn−1

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Chapter 8, Problem 7SE

Chapter 8, Problem 9SE

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The solution of the simultaneous system of recurrence relations a n = a n − 1 + b n − 1 a n d b n = a n − 1 − b n − 1

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To calculate: The solution of the simultaneous system of recurrence relations an=an−1+bn−1 and bn=an−1−bn−1

Want to see the full answer?

Chapter 8 Solutions

To calculate:

The solution of the simultaneous system of recurrence relations

an=an−1+bn−1 and bn=an−1−bn−1