Define a sequence of real numbers (xn) as follows: Let x₁ = 2, and supposing that an has been defined, define 1 2 3+1 = 2 ( x x + ²) Xn+1 . (a) Prove that x2 is always greater than or equal to 2, and then use this to prove that xnxn+1 ≥ 0. [So (n) is decreasing.] Conclude that lim = √2. in (b) For any real number c> 0, define a sequence (yn) so that (yn) converges to √c.

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