The intensity of light LLL measured at a depth rrr inside a specific mineral solution is modeled by the function
L(r)=(4+αr)−2,∣αr∣<4 L(r) = (4 + \alpha r)^{-2}, \quad |\alpha r| < 4 L(r)=(4+αr)−2,∣αr∣<4where α\alphaα is a non-zero attenuation constant. The series expansion for this model is given by
L(r)=A+Br+Cr2+Dr3+… L(r) = A + Br + Cr^2 + Dr^3 + \dots L(r)=A+Br+Cr2+Dr3+…where A,B,CA, B, CA,B,C and DDD are constants.
Find the value of AAA.
Given that C=−9BC = -9BC=−9B
show that α2−24α=0\alpha^2 - 24\alpha = 0α2−24α=0.
Hence (i) find the value of α\alphaα (ii) find the value of DDD.
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.
