10 The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by \(u _ { 1 } = 2\) and \(u _ { n + 1 } = \frac { u _ { n } } { 1 + u _ { n } }\) for \(n \geqslant 1\).
- Find \(u _ { 2 }\) and \(u _ { 3 }\), and show that \(u _ { 4 } = \frac { 2 } { 7 }\).
- Hence suggest an expression for \(u _ { n }\).
- Use induction to prove that your answer to part (ii) is correct.