Mathematics, 05.03.2020 01:08, ant5784tgi

(a) Prove that the sequence defined by x1 = 3 and xn+1 = 1 4 − xn converges. 60 Chapter 2. Sequences and Series (b) Now that we know lim xn exists, explain why lim xn+1 must also exist and equal the same value. (c) Take the limit of each side of the recursive equation in part (a) to explicitly compute lim xn.

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(a) Prove that the sequence defined by x1 = 3 and xn+1 = 1 4 − xn converges. 60 Chapter 2. Sequences...