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Prove the property of the Fibonacci numbers, F(n) = 5(n 4) + 3F(n-5), for n ≥6

Prove the property of the Fibonacci numbers, F(n) = 5(n 4) + 3F(n-5), for n ≥6

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Prove the property of the Fibonacci numbers:** \[ F(n) = 5F(n-4) + 3F(n-5), \, \text{for} \, n \geq 6 \] This equation presents a property of the Fibonacci sequence, where \( F(n) \) denotes the nth Fibonacci number. The property holds for values of \( n \) greater than or equal to 6.
Transcribed Image Text:**Prove the property of the Fibonacci numbers:** \[ F(n) = 5F(n-4) + 3F(n-5), \, \text{for} \, n \geq 6 \] This equation presents a property of the Fibonacci sequence, where \( F(n) \) denotes the nth Fibonacci number. The property holds for values of \( n \) greater than or equal to 6.
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Step 1

We have to prove the property of the given Fibonacci numbers

F(n) = 5F(n-4) + 3F(n-5) ,  for n≥6

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