OCR C4 2006 January — Question 7

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2006
SessionJanuary
TopicGeneralised Binomial Theorem and Partial Fractions

7 The expression \(\frac { 11 + 8 x } { ( 2 - x ) ( 1 + x ) ^ { 2 } }\) is denoted by \(\mathrm { f } ( x )\).
  1. Express \(\mathrm { f } ( x )\) in the form \(\frac { A } { 2 - x } + \frac { B } { 1 + x } + \frac { C } { ( 1 + x ) ^ { 2 } }\), where \(A , B\) and \(C\) are constants.
  2. Given that \(| x | < 1\), find the first 3 terms in the expansion of \(\mathrm { f } ( x )\) in ascending powers of \(x\).