Use the binomial expansion to expand
(16+2v)−12∣v∣<8 (16 + 2v)^{-\frac{1}{2}} \quad |v| < 8 (16+2v)−21∣v∣<8in ascending powers of vvv, up to and including the term in v2v^2v2, giving each coefficient as a fully simplified fraction.
The pressure PPP in a pneumatic cylinder is modeled by the function
P(v)=12+kv16+2vwhere k is a constant and ∣v∣<8 P(v) = \frac{12 + kv}{\sqrt{16 + 2v}} \quad \text{where } k \text{ is a constant and } |v| < 8 P(v)=16+2v12+kvwhere k is a constant and ∣v∣<8Given that the series expansion of P(v)P(v)P(v), in ascending powers of vvv, is
3+916v+qv2+…where q is a constant 3 + \frac{9}{16}v + qv^2 + \dots \quad \text{where } q \text{ is a constant} 3+169v+qv2+…where q is a constantfind the value of kkk,
find the value 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.
