(i)[3]
Determine the value of $\alpha$ correct to $3$ decimal places, and give the result from each iteration to $5$ decimal places.
(ii)[2]
State an equation that $\alpha$ satisfies and hence determine the exact value of $\alpha$.
Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
Starting from $x_1 = 2$, the values generated by the iterative formula $x_{n+1} = 2 + \frac{4}{x_n^2 + 2x_n + 4}$ approach $\alpha$.