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
308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.