11. The Lucas numbers satisfy the recurrence relation Links L, = L-1 + Lp-2» and the initial conditions L = 2 and L, = 1. a) Show that L, = fn-1 +fn+1 for n = 2, 3 ..., where f, is the nth Fibonacci...

Plz solve both parts( a and b)

11. The Lucas numbers satisfy the recurrence relation<br>Links<br>L, = L-1 + Lp-2»<br>and the initial conditions L = 2 and L, = 1.<br>a) Show that L, = fn-1 +fn+1 for n = 2, 3 ..., where f,<br>is the nth Fibonacci number.<br>b) Find an explicit formula for the Lucas numbers.<br>

Extracted text: 11. The Lucas numbers satisfy the recurrence relation Links L, = L-1 + Lp-2» and the initial conditions L = 2 and L, = 1. a) Show that L, = fn-1 +fn+1 for n = 2, 3 ..., where f, is the nth Fibonacci number. b) Find an explicit formula for the Lucas numbers.

Jun 04, 2022

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11. The Lucas numbers satisfy the recurrence relation Links L, = L-1 + Lp-2» and the initial conditions L = 2 and L, = 1. a) Show that L, = fn-1 +fn+1 for n = 2, 3 ..., where f, is the nth Fibonacci...

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