Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The sequence $x_1, x_2, x_3, \dots$ defined by $x_1 = 1$, $x_{n+1} = \frac{x_n}{\ln(2x_n)}$ tends to the limit $\alpha$.
(i)[3]
Apply the iterative formula to determine the value of $\alpha$ correct to $4$ significant figures. Record the result of each iteration to $6$ significant figures.
(ii)[2]
State the equation that $\alpha$ satisfies and then deduce the exact value of $\alpha$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Carry out the iteration correctly on at least one occasion” …