1. Let an be a sequence of real numbers defined by aj = V2 and an+1 = 12+ an. Prove by induction that an < 2 for all n >
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1. Let an be a sequence of real numbers defined by aj = V2 and an+1 = 12+ an. Prove by induction that an < 2 for all n >
1. Let an be a sequence of real numbers defined by aj = V2 and an+1 = 12+ an. Prove by induction that an < 2 for all n > 1. 2. Prove that the square of an odd integer is odd by using: (a) a direct proof; (b) a proof by contradiction; (c) is it possible to use induction to prove this statement? Explain.
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