(i)[3]
Determine $\alpha$ correct to $2$ decimal places, and give the outcome of each iteration correct to $4$ decimal places.
(ii)[3]
Find the exact value of $\alpha$.
Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The terms generated by the iterative rule $x_{n+1} = \frac{2x_n^2 + x_n + 9}{(x_n + 1)^2}$, beginning with $x_1 = 2$, settle to $\alpha$.