Exam-Style Problem
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June 2013 p32 q2
1811
The sequence of values given by the iterative formula
\(x_{n+1} = \frac{x_n(x_n^3 + 100)}{2(x_n^3 + 25)}\),
with initial value \(x_1 = 3.5\), converges to \(\alpha\).
- Use this formula to calculate \(\alpha\) correct to 4 decimal places, showing the result of each iteration to 6 decimal places.
- State an equation satisfied by \(\alpha\) and hence find the exact value of \(\alpha\).
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