The reaction rate R R\,R of a biochemical catalyst depends on its concentration ccc (in mol dm−3^{-3}−3) according to the model
R(c)=1+8c23,∣c∣<18 R(c) = \sqrt[3]{1 + 8c^2}, \quad |c| < \frac{1}{\sqrt{8}} R(c)=31+8c2,∣c∣<81Find, in ascending powers of ccc, the first three non-zero terms of the binomial series expansion of R(c)R(c)R(c), giving each coefficient as a simplified fraction.
By substituting c=14\displaystyle c = \frac{1}{4}c=41 into the expansion from part (a), find a rational approximation to k33k \sqrt[3]{3}k33, where k k\,k is a constant you must determine.
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.
