6. Let a, = 1 and for n > 2 let an = (,),-1. Prove that 6 an = for all n E N. n2
6. Let a, = 1 and for n > 2 let an = (,"),-1. Prove that 6 an = for all n E N. n2 + 3n + 2 Let Co = C1 = 1 and for n > 3 let Cn = Ca-1 + Ca-2 + 1. (a) Make a table of values of Co, C1, . ... Cin. Guess a formula for co + + . . . + Cn and prove it. (b) Use the Strong Principle of Mathematical Induction to prove that n-1 Cn > 191 00 for each integer n > 0
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