Generalised Binomial Theorem and Partial Fractions
3
Find the binomial expansion of \(( 1 - x ) ^ { - 1 }\) up to and including the term in \(x ^ { 2 }\).
Express \(\frac { 3 x - 1 } { ( 1 - x ) ( 2 - 3 x ) }\) in the form \(\frac { A } { 1 - x } + \frac { B } { 2 - 3 x }\), where \(A\) and \(B\) are integers.
Find the binomial expansion of \(\frac { 3 x - 1 } { ( 1 - x ) ( 2 - 3 x ) }\) up to and including the term in \(x ^ { 2 }\).
Find the range of values of \(x\) for which the binomial expansion of \(\frac { 3 x - 1 } { ( 1 - x ) ( 2 - 3 x ) }\) is valid.