(i)[3]
Use the formula to determine $\alpha$ correct to $4$ decimal places. Record each iteration to $6$ decimal places.
(ii)[2]
State an equation that $\alpha$ satisfies and hence obtain the exact value of $\alpha$.
Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The values in the sequence produced by the iterative formula $x_{n+1} = \frac{2x_n^6 + 12x_n}{3x_n^5 + 8}$, starting from $x_1 = 2$, converges to $\alpha$.