Generalised Binomial Theorem and Partial Fractions
3
Express \(\frac { x } { ( 1 + x ) ( 1 - 2 x ) }\) in partial fractions.
Hence use binomial expansions to show that \(\frac { x } { ( 1 + x ) ( 1 - 2 x ) } = a x + b x ^ { 2 } + \ldots\), where \(a\) and \(b\) are
constants to be determined. constants to be determined.
State the set of values of \(x\) for which the expansion is valid.