In a study of fluid dynamics, the pressure PPP within a vessel at a specific depth hhh is modeled by the expression
(4+kh)5 (4 + kh)^5 (4+kh)5where kkk is a positive constant. For small values of hhh, the pressure can be approximated by the binomial expansion
P(h)=A+Bh+Ch2+Dh3+⋯ P(h) = A + Bh + Ch^2 + Dh^3 + \cdots P(h)=A+Bh+Ch2+Dh3+⋯where A,B,CA, B, CA,B,C and DDD are constants.
Find the value of AAA.
Given that B=2DB = 2DB=2D and k>0k > 0k>0,
Find:
(i) the value of kkk
(ii) the value of CCC
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.
