(i)[3]
Employ this iterative formula to find $\alpha$ correct to $2$ decimal places, with each iteration written to $4$ decimal places.
(ii)[2]
Write down an equation satisfied by $\alpha$ and hence show that $\alpha = \sqrt[5]{20}$.
Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The values produced by the iterative relation $x_{n+1} = \frac{7x_n}{8} + \frac{5}{2x_n^4}$, starting from $x_1 = 1.7$, approach $\alpha$.