Chapter 8.2, Problem 11E

The Lucas numbers satisfy the recurrence relation $L_n=L_{n-1}+L_{n-2}$and the initial conditions $L_0=2$and $L_1=1$ .

a) Show that $L_n=f_{n-1}+f_{n+1}$for n = 2, 3,..., where $f_n$ is the nth Fibonacci number.

b) Find an explicit formula for the Lucas numbers.