1 The sequence \(\left\{ u _ { n } \right\}\) is defined by \(u _ { 1 } = 2\) and \(u _ { n + 1 } = \frac { 12 } { 1 + u _ { n } }\) for \(n \geq 1\).
Given that the sequence converges, with limit \(\alpha\), determine the value of \(\alpha\).