Consider the sequence {an}, defined by a1 = 2 and an = E (2an-1 + 5) for n > 2. Use induction to prove that an 21 for all n E J.

10, a2 The sequence {an} is defined recursively by a 16, and an = by mathematical induction that an = 3.2" + 4 for all n € N. = = 3an 12an-2 for n ≥ 3. Prove

Let {an}∞ n=0 be a sequence such that a0 = 2, a1 = 4, an = 4an−1 − 3an−2 for n ≥ 2. (a) Calculate a2, a3, a4, a5 and then guess a possible direct formula for an, n ≥ 0. (b) Use strong mathematical induction to prove your formula.

Let b1, b2, b3,... be the sequence of numbers defined by b1 = 1, and b, V6 + bn-1 if n > 2. Prove that 0 1.