Let (f_n) denote the fibonacci sequence. define the lucas sequence l_0 = 2, l_1 = 1, and for n greaterthanorequalto 1 define l_n+1 = l_n + l_n-1. (for some proofs you may want to use the second principle of induction stated in the problem section of by chapter 18 as theorem 18.9.) (a) calculate l_1, l_10. (b) calculate l_n - f_n - 1, for n greaterthanorequalto 1. find a remarkable pattern in this list of numbers. state it clearly and prove it by induction (c) calculate f_n + l_n. find a remarkable pattern in this list of clearly and prove it using part (b).