(2) Let an be the sequence defined by: a₁ = 1 a2 = 2 an an-1 + 2an-2 for n ≥ 3. (a) Find a3,.. (b) Use induction to prove that an > 0 for all n € N. an (c) Use induction to prove that an+1 (d) Use (b) and (c) to conclude that an < an+1 for all n € N. .... ag. < 1 for all n € N.

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