2. [40 pts.] Induction proofs (a) (20 pts.] Use induction on n to prove that for all integers n > 1, -12 = n(n+1)(2n + 1)/6. (b) (20 pts. Consider the infinite sequence of integers fo, fi, f2, ..., defined by fo = 1, 1 = 2 and Sn = fn-1 + fn-2 for all n > 2. Use induction on n to prove that fr. 2" for all n 1