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Use the characteristic root technique to find a closed-formula for the Fibonacci numbers. Your formula should look like: Fn = ar + br for some numbers a, b, r1, r2 E R that you determine.

Use the characteristic root technique to find a closed-formula for the Fibonacci numbers. Your formula should look like: Fn = ar + br for some numbers a, b, r1, r2 E R that you determine.

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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Problem 1 Use the characteristic root technique to find a closed-formula for the Fibonacci numbers. Your formula should look like: Fn = ar + br for some numbers a, b, r₁, r2 € R that you determine. Hint: A complete solution involves both using the quadratic formula and solving a 2 × 2 system of linear equations. Note: This is a famous result with an easily-researched answer. So, the important part is showing your work and making sure you are familiar with tools like the quadratic formula.
Transcribed Image Text:Problem 1 Use the characteristic root technique to find a closed-formula for the Fibonacci numbers. Your formula should look like: Fn = ar + br for some numbers a, b, r₁, r2 € R that you determine. Hint: A complete solution involves both using the quadratic formula and solving a 2 × 2 system of linear equations. Note: This is a famous result with an easily-researched answer. So, the important part is showing your work and making sure you are familiar with tools like the quadratic formula.
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