A researcher models the intensity I I\,I of a signal as it penetrates a specific material of thickness x x\,x cm. The model is given by
I(x)=(1+23x)−3for ∣x∣<32 I(x) = \left(1 + \frac{2}{3}x\right)^{-3} \quad \text{for } |x| < \frac{3}{2} I(x)=(1+32x)−3for ∣x∣<23Find the binomial expansion of I(x)I(x)I(x) in ascending powers of x x\,x up to and including the term in x3x^3x3. Simplify each coefficient fully and present them as exact fractions.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
