Consider the sequence <xₙ>, n ≥ 0, defined by the recurrence relation xₙ₊₁ = c…
GATE · 2007 · IT
Consider the sequence <xₙ>, n ≥ 0, defined by the recurrence relation
xₙ₊₁ = c xₙ² - 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))/(2c)
- B.
(1 - √(1 + 8c))/(2c)
- C.
2
- D.
2/(2c - 1)
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