Fibonacci numbers F1, F2, F3, . . . are defined by the rule: F1 = F2 = 1 and Fk = Fk−2 + Fk−1 for k > 2. Lucas numbers L1, L2, L3, . . . are defined in a similar way by the rule: L1 = 1, L2 = 3 and Lk = Lk−2 + Lk−1 for k > 2. Show that Fibonacci and Lucas numbers satisfy the following equality for all n ≥ 2 Ln = Fn−1 + Fn+1.

Fibonacci numbers F1, F2, F3, . . . are defined by the rule: F1 = F2 = 1 and Fk = Fk−2 + Fk−1 for k > 2. Lucas numbers L1, L2, L3, . . . are defined in a similar way by the rule: L1 = 1, L2 = 3 and Lk = Lk−2 + Lk−1 for k > 2. Show that Fibonacci and Lucas numbers satisfy the following equality for all n ≥ 2 Ln = Fn−1 + Fn+1.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter19: Probabilistic Dynamic Programming

Section19.3: How To Maximize The Probability Of A Favorable Event Occurring

Problem 1P

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