A-LevelMathematicsNumerical methods9709/22 · Oct/Nov 2019 · Q45 Marks
The sequence x₁, x₂, x₃, ... defined by x₁ = 1, xn+1 = xn / ln(2xn) converges to the value α.
- (i)Use the iterative formula to find the value of α correct to 4 significant figures. Give the result of each iteration to 6 significant figures.[3]
- (ii)State an equation satisfied by α and hence determine the exact value of α.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [M1] Use iteration correctly at least once (Must see correct attempt at x₃)
- [A1] Obtain final answer 1.359
- [A1] Show sufficient iterations to 6 sf to justify answer or show sign change in interval [1.3585, 1.3595] (Answer required to exactly 4 sf, Must see to at least x₅)
- [B1] Form correct equation in x (or α) (x = x / ln(2x) OE)
- [B1] Obtain e/2
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