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Competitive Stats
Q37Section ST (Statistics (Q11–Q65))37 of 65

Convergence of x_{n+1} = 2 - sqrt(4 - x_n)

Let x1∈(0,4)x_1 \in (0, 4) and consider the sequence {xn}n≥1\{x_n\}_{n \ge 1} defined iteratively by xn+1=2−(4−xn)1/2x_{n+1} = 2 - (4 - x_n)^{1/2}, n≥1n \ge 1. Consider the following statements: (I) {xn}\{x_n\} converges to 0. (II) {xn+1/xn}\{x_{n+1}/x_n\} converges to 1/41/4. Which of the following statements is correct?

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