The Lucas numbers, named after Franfois-Eduoard-Anatole Lucas are defined recursively by Ln =Ln-1 + Ln-2, n≥3 with L1 = 1 and L2 = 3 . They satisfy the same recurrence relation as the Fibonacci numbers, but the two initial values are different. Prove that L2n − Ln+1Ln-1 = 5(−1)n , n≥2.
The Lucas numbers, named after Franfois-Eduoard-Anatole Lucas are defined recursively by Ln =Ln-1 + Ln-2, n≥3 with L1 = 1 and L2 = 3 . They satisfy the same recurrence relation as the Fibonacci numbers, but the two initial values are different. Prove that L2n − Ln+1Ln-1 = 5(−1)n , n≥2.
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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The Lucas numbers, named after Franfois-Eduoard-Anatole Lucas
are defined recursively by
Ln =Ln-1 + Ln-2, n≥3
with L1 = 1 and L2 = 3 . They satisfy the same recurrence relation as the Fibonacci numbers, but the two initial values are different.
Prove that
L2n − Ln+1Ln-1 = 5(−1)n , n≥2.
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