2. Let the sequence (xn) be recursively defined by x₁ = 1 and n+1 (a) Prove by induction that 1 ≤ n < 2 for all nЄN. (b) Prove that (x) is increasing. (c) Prove that (xn) converges, and determine lim (xn). x² +6 'n 5 for all n € N.

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