CAIE P2 2017 June — Question 4

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2017
SessionJune
TopicFixed Point Iteration

4 The sequence of values given by the iterative formula $$x _ { n + 1 } = \frac { 2 x _ { n } ^ { 2 } + x _ { n } + 9 } { \left( x _ { n } + 1 \right) ^ { 2 } }$$ with \(x _ { 1 } = 2\), converges to \(\alpha\).
  1. Find the value of \(\alpha\) correct to 2 decimal places, giving the result of each iteration to 4 decimal places.
  2. Determine the exact value of \(\alpha\).