GATE | Gate IT 2007 | Question 74

Consider the sequence <x_n>, n>= 0 defined by the recurrence relation x_{n + 1} = c . x_n²– 2, where c > 0.

Suppose there exists a non-empty, open interval (a, b) such that for all x₀ satisfying a < x₀ < b, the sequence converges to a limit. The sequence converges to the value?
(A) (1 + (1 + 8c)^1/2)/2c
(B) (1 – (1 + 8c)^1/2)/2c
(C) 2
(D) 2/(2c-1)


Answer: (B)

Explanation:

This solution is contributed by Anil Saikrishna Devarasetty.

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