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C. The Fibonacci numbers (Fn)n21 are defined by the recurrence F₁ = 1, F2 = 1, Fn = Fn-1 + Fn-2 for n ≥ 3. Thus, the first Fibonacci numbers are F₁ = 1, F₂ = 1, F3 = 2, F₁ = 3, F5 = 5, F68, F7 = 13. The Fibonacci numbers appear in many places in nature and art. Prove that for n ≥ 1, F₁+F₂ + + Fn = Fn+2 -1.

C. The Fibonacci numbers (Fn)n21 are defined by the recurrence F₁ = 1, F2 = 1, Fn = Fn-1 + Fn-2 for n ≥ 3. Thus, the first Fibonacci numbers are F₁ = 1, F₂ = 1, F3 = 2, F₁ = 3, F5 = 5, F68, F7 = 13. The Fibonacci numbers appear in many places in nature and art. Prove that for n ≥ 1, F₁+F₂ + + Fn = Fn+2 -1.

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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Please solve the following discrete proof 

C. The Fibonacci numbers (Fn)n>1 are defined by the recurrence F₁ = 1, F2 = 1, Fn Fn-1 + Fn-2 for n ≥ 3. = Thus, the first Fibonacci numbers are F₁ = 1, F₂ = 1, F3 = 2, F₁ = 3, F5 = 5, F6 = 8, F7 = 13. The Fibonacci numbers appear in many places in nature and art. Prove that for n ≥ 1, F₁+F₂ + + Fn = Fn+2 -1.
Transcribed Image Text:C. The Fibonacci numbers (Fn)n>1 are defined by the recurrence F₁ = 1, F2 = 1, Fn Fn-1 + Fn-2 for n ≥ 3. = Thus, the first Fibonacci numbers are F₁ = 1, F₂ = 1, F3 = 2, F₁ = 3, F5 = 5, F6 = 8, F7 = 13. The Fibonacci numbers appear in many places in nature and art. Prove that for n ≥ 1, F₁+F₂ + + Fn = Fn+2 -1.
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