7 Irrational numbers can be modelled by sequences \(\left\{ u _ { n } \right\}\) of rational numbers of the form $$u _ { 0 } = 1 \text { and } u _ { n + 1 } = a + \frac { 1 } { b + u _ { n } } \text { for } n \geqslant 0 \text {, }$$ where \(a\) and \(b\) are non-negative integer constants.

1. (a) The constants \(a = 1\) and \(b = 0\) produce the irrational number \(\omega\). State the value of \(\omega\) correct to six decimal places.
   (b) By setting \(u _ { n + 1 }\) and \(u _ { n }\) equal to \(\omega\), determine the exact value of \(\omega\).
2. Use the method of part (i) (b) to find the exact value of the irrational number produced by taking \(a = 0\) and \(b = 2\).
3. Find positive integers \(a\) and \(b\) which would produce the irrational number \(2 + \sqrt { 10 }\). \section*{END OF QUESTION PAPER}