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Let fn be the n-th Fibonacci number of Example 3c in 8.1, k=n k=n = An Σ=1+2+. .+ n₂ =k²= 1² +2²+. k=1 k=1 by definition fo = Ao = Bo = 0. (a) Give a recursive definition of the numbers fn, An, Bn with n20 - + n²;

Let fn be the n-th Fibonacci number of Example 3c in 8.1, k=n k=n = An Σ=1+2+. .+ n₂ =k²= 1² +2²+. k=1 k=1 by definition fo = Ao = Bo = 0. (a) Give a recursive definition of the numbers fn, An, Bn with n20 - + n²;

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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Let fn be the n-th Fibonacci number of Example 3c in 8.1, k=n k=n An= k = 1 + 2 + ... + m₂ -E- B₁=k²= 1² +2²+...+n²; k=1 k=1 by definition fo = Ao = Bo = 0. (a) Give a recursive definition of the numbers fn, An, Bn with n20 (b) Use mathematical induction and only part (a) to show that fn, An, Bn <5" for all n ≥ 0
Transcribed Image Text:Let fn be the n-th Fibonacci number of Example 3c in 8.1, k=n k=n An= k = 1 + 2 + ... + m₂ -E- B₁=k²= 1² +2²+...+n²; k=1 k=1 by definition fo = Ao = Bo = 0. (a) Give a recursive definition of the numbers fn, An, Bn with n20 (b) Use mathematical induction and only part (a) to show that fn, An, Bn <5" for all n ≥ 0
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