1．（a）For \(| y | < 1\) ，write down the binomial series expansion of \(( 1 - y ) ^ { - 2 }\) in ascending powers of \(y\) up to and including the term in \(y ^ { 3 }\) ．
（b）Hence，or otherwise，show that $$1 + \frac { 2 x } { 1 + x } + \frac { 3 x ^ { 2 } } { ( 1 + x ) ^ { 2 } } + \ldots + \frac { r x ^ { r - 1 } } { ( 1 + x ) ^ { r - 1 } } + \ldots$$ can be written in the form \(( a + x ) ^ { n }\) ．Write down the values of the integers \(a\) and \(n\) ．
（c）Find the set of values of \(x\) for which the series in part（b）is convergent．