Expand \(( 1 + 2 x ) ^ { \frac { 1 } { 2 } }\) as a series in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\).
Hence find the expansion of \(\frac { ( 1 + 2 x ) ^ { \frac { 1 } { 2 } } } { ( 1 + x ) ^ { 3 } }\) as a series in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\).
State the set of values of \(x\) for which the expansion in part (ii) is valid.