CAIE P3 2002 June — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2002
SessionJune
TopicFixed Point Iteration

4 The sequence of values given by the iterative formula $$x _ { n + 1 } = \frac { 2 } { 3 } \left( x _ { n } + \frac { 1 } { x _ { n } ^ { 2 } } \right)$$ with initial value \(x _ { 1 } = 1\), converges to \(\alpha\).
  1. Use this formula to find \(\alpha\) correct to 2 decimal places, showing the result of each iteration.
  2. State an equation satisfied by \(\alpha\), and hence find the exact value of \(\alpha\).