The Fibonacci numbers are defined recursively by F, = 1, F2 = 1, and F = Fn-1 + Fn-2 for n 2 3. We can prove facts about F using induction by exploiting the recurrence F = Fn-1 + Fn-2, that is, each term is the sum of the two consecutive previous terms. a. Find F for n = 3,4,5,6, and 7. b. Prove F, + F2 + …·+ F, = Fn+2 - 1 for all n > 1. Prove F? + F + .…+ F = F„Fn+1 for all n > 1. K11. C.

The Fibonacci numbers are defined recursively by F, = 1, F2 = 1, and F = Fn-1 + Fn-2 for n 2 3. We can prove facts about F using induction by exploiting the recurrence F = Fn-1 + Fn-2, that is, each term is the sum of the two consecutive previous terms. a. Find F for n = 3,4,5,6, and 7. b. Prove F, + F2 + …·+ F, = Fn+2 - 1 for all n > 1. Prove F? + F + .…+ F = F„Fn+1 for all n > 1. K11. C.

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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