3 In this question you should assume that \(- 1 < x < 1\).
- For the binomial expansion of \(( 1 - x ) ^ { - 2 }\)
- find and simplify the first four terms,
- write down the term in \(x ^ { n }\).
- Write down the sum to infinity of the series \(1 + x + x ^ { 2 } + x ^ { 3 } + \ldots\).
- Hence or otherwise find and simplify an expression for \(2 + 3 x + 4 x ^ { 2 } + 5 x ^ { 3 } + \ldots\) in the form \(\frac { a - x } { ( b - x ) ^ { 2 } }\) where \(a\) and \(b\) are constants to be determined.