CAIE P3 2012 November — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionNovember
TopicGeneralised Binomial Theorem
TypeArithmetic/geometric progression coefficients

4 When \(( 1 + a x ) ^ { - 2 }\), where \(a\) is a positive constant, is expanded in ascending powers of \(x\), the coefficients of \(x\) and \(x ^ { 3 }\) are equal.
  1. Find the exact value of \(a\).
  2. When \(a\) has this value, obtain the expansion up to and including the term in \(x ^ { 2 }\), simplifying the coefficients.