Let {an} be the sequence defined recursively by a0 = 0, an+1 = 2 + an Thus, a1 = 2, a2 =
Chapter 10, Problem 84(choose chapter or problem)
Let {an} be the sequence defined recursively by a0 = 0, an+1 = 2 + an Thus, a1 = 2, a2 = 2 + 2, a3 = 2 + 2 + 2,....(a) Show that if an < 2, then an+1 < 2. Conclude by induction that an < 2 for all n. (b) Show that if an < 2, then an an+1. Conclude by induction that {an} is increasing. (c) Use (a) and (b) to conclude thatL = lim n an exists. Then compute
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