CAIE P3 2023 November — Question 10

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2023
SessionNovember
TopicGeneralised Binomial Theorem and Partial Fractions

10 Let \(\mathrm { f } ( x ) = \frac { 24 x + 13 } { ( 1 - 2 x ) ( 2 + x ) ^ { 2 } }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Hence obtain the expansion of \(\mathrm { f } ( x )\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\).
  3. State the set of values of \(x\) for which the expansion in (b) is valid.