The population density ρ(r)\rho(r)ρ(r) of a certain bacterial colony as a function of the distance r r\,r from its center is modeled by the function ρ(r)=(3+2r)−3\rho(r) = (3 + 2r)^{-3}ρ(r)=(3+2r)−3 for ∣r∣<1.5|r| < 1.5∣r∣<1.5.
Find the binomial expansion of ρ(r)\rho(r)ρ(r) in ascending powers of r r\,r up to and including the term in r3r^3r3, fully simplifying each coefficient.
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.
