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1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 239

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)5

where 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.

a.

Find the value of AAA.

[1]
b.

Given that B=2DB = 2DB=2D and k>0k > 0k>0,

Find:

(i) the value of kkk

(ii) the value of CCC

[6]
Markscheme

1.7 D: Sequences and series Questions

  1. A Level
  2. /Maths
  3. /1.7 D: Sequences and series

308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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