(i)[3]
Use this formula to find $\alpha$ correct to 4 decimal places, showing each iteration to 6 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
The value sequence generated by the iterative formula $x_{n+1} = \dfrac{x_n(x_n^3 + 100)}{2(x_n^3 + 25)}$, and starting from $x_1 = 3.5$, converges to $\alpha$.