n- Let fn be the nth Fibonacci number, i.e. we will let fo = 0, f...

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n- Let fn be the nth Fibonacci number, i.e. we will let fo = 0, f = 1, and then fn = fn1 + n2 for all n 2 (so f = 1, f3 = 2, f4 = 5, f5 = 8, f6 = 13, and so forth). Prove using induction that f2 n 1 fn = 5 1+5 2 n 5 2 (hint: most of the time in a proof by induction you prove one base case (in this case it might be P(0), and then assume P(n) and try to prove P(n + 1)). Another valid way to prove something by induction is to prove two base cases (P(0) and P(1)), and then prove that Vn N, [(P(n 1) and P(n)) P(n+1)]. Before you approach this problem, think about why this would be sufficient to prove VP(n). - n- Let fn be the nth Fibonacci number, i.e. we will let fo = 0, f = 1, and then fn = fn1 + n2 for all n 2 (so f = 1, f3 = 2, f4 = 5, f5 = 8, f6 = 13, and so forth). Prove using induction that f2 n 1 fn = 5 1+5 2 n 5 2 (hint: most of the time in a proof by induction you prove one base case (in this case it might be P(0), and then assume P(n) and try to prove P(n + 1)). Another valid way to prove something by induction is to prove two base cases (P(0) and P(1)), and then prove that Vn N, [(P(n 1) and P(n)) P(n+1)]. Before you approach this problem, think about why this would be sufficient to prove VP(n). -