The Lucas numbers satisfy the recurrence relation Ln=Ln-1+ Ln-2, and the initial conditions are Lo = 2 and 4₁ = 1. Click and drag statements to find an explicit formula for the Lucas numbers. L₁ = α₂ -a for some constants a, and a₂. The recurrence relation L₁= L-1 + L₂-2 has characteristic equation 1+√√5 2+7-1=0. Its roots are >= - L-a(1+√³)* + a₂ (1-√³) 1+√√5 1-√√5 L₁ = 2 for some constants a, and a₂. 1+√ 4- (1+³)+(1-³). L₁=2 and L₁=1-a₁=1 and a₂ = 1. L₂ = 4-(+)-(-). L₁= 2 and L₁ = 1 → a₁ = 1 and ₂ = 1. L = The recurrence relation L=L+L2 has characteristic equation 1+√5 2 2-1=0. Its roots are >=
The Lucas numbers satisfy the recurrence relation Ln=Ln-1+ Ln-2, and the initial conditions are Lo = 2 and 4₁ = 1. Click and drag statements to find an explicit formula for the Lucas numbers. L₁ = α₂ -a for some constants a, and a₂. The recurrence relation L₁= L-1 + L₂-2 has characteristic equation 1+√√5 2+7-1=0. Its roots are >= - L-a(1+√³)* + a₂ (1-√³) 1+√√5 1-√√5 L₁ = 2 for some constants a, and a₂. 1+√ 4- (1+³)+(1-³). L₁=2 and L₁=1-a₁=1 and a₂ = 1. L₂ = 4-(+)-(-). L₁= 2 and L₁ = 1 → a₁ = 1 and ₂ = 1. L = The recurrence relation L=L+L2 has characteristic equation 1+√5 2 2-1=0. Its roots are >=
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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Transcribed Image Text:The Lucas numbers satisfy the recurrence relation Ln=Ln-1+ Ln-2, and the initial conditions are Lo = 2 and L₁ = 1.
Click and drag statements to find an explicit formula for the Lucas numbers.
L = a (¹+√³)² - a₂ (1-√³)
+√√5
for some constants α₁ and ₂.
The recurrence relation L₂= L-1 + L-2 has characteristic equation
1+√√5
2
²+1=0. Its roots are r =
1-√√√5
L₂ = a (¹+√³)² + a₂ (¹ = √³)*
2
for some constants a₁ and ₂.
1+
1.4. - (¹ + √/³)* + (¹-1/³).
Lo=2 and L₁=1 → a= 1 and ₂ = 1. L₁ =
4- - (¹ + ³) - (¹ -- ).
Lo=2 and L₁ = 1 → α₁ = 1 and α₂ = 1. L₁ =
The recurrence relation L₂=Ln-1 + Ln-2 has characteristic equation
1+√√5
2
72-1=0. Its roots are r =
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