Let D(v)D(v)D(v) be a function representing the density of a gas relative to its volume vvv, defined by
D(v)=(2−v8)10 D(v) = \left(2 - \frac{v}{8}\right)^{10} D(v)=(2−8v)10Find the first 4 terms of the binomial expansion of D(v)D(v)D(v) in ascending powers of vvv, giving each coefficient as an integer.
A related physical quantity Q Q\,Q is derived from the density function such that
Q=(3+2v)2D(v) Q = \left(3 + \frac{2}{v}\right)^2 D(v) Q=(3+v2)2D(v)Hence, find the constant term in the series expansion of QQQ.
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.
