Edexcel C34 2015 June — Question 2

Exam BoardEdexcel
ModuleC34 (Core Mathematics 3 & 4)
Year2015
SessionJune
TopicGeneralised Binomial Theorem and Partial Fractions

2. Given that $$\frac { 4 \left( x ^ { 2 } + 6 \right) } { ( 1 - 2 x ) ( 2 + x ) ^ { 2 } } \equiv \frac { A } { ( 1 - 2 x ) } + \frac { B } { ( 2 + x ) } + \frac { C } { ( 2 + x ) ^ { 2 } }$$
  1. find the values of the constants \(A\) and \(C\) and show that \(B = 0\)
    (4)
  2. Hence, or otherwise, find the series expansion of $$\frac { 4 \left( x ^ { 2 } + 6 \right) } { ( 1 - 2 x ) ( 2 + x ) ^ { 2 } } , \quad | x | < \frac { 1 } { 2 }$$ in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), simplifying each term.
    (5)