An engineering model for the structural density ρ \rho\,ρ of a composite material, relative to a depth xxx, is given by the binomial expansion of (3+kx)6(3 + kx)^6(3+kx)6 in ascending powers of xxx. The expansion is written in the form:
ρ=c0+c1x+c2x2+c3x3+… \rho = c_0 + c_1 x + c_2 x^2 + c_3 x^3 + \dots ρ=c0+c1x+c2x2+c3x3+…where c0,c1,c2, c_0, c_1, c_2,\,c0,c1,c2, and c3 c_3\,c3 are constants.
Find the value of c0c_0c0.
Given that:
Find:
(i) the value of kkk
(ii) the value of c2c_2c2
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.
