Here is my problem, two parts.

The Lucas sequence is defined by

(L_n) = {1,3,4,7,11,18,...}

where the successive terms is found by adding the two previous terms.

1.) Show that the general term, or the nth term of the Lucas sequence is

L_n = [(1 + SQRT(5))/2]^n + [(1 - SQRT(5))/2]^n = (alpha)^n + (beta)^n

2.) Prove the formula for the general term using mathematical induction.

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Thank You!