The strength of a magnetic field BBB, measured in microteslas, at a distance rrr cm from a specific electronic component is modeled by the function:
B(r)=(10r+3)(1−14r)12,0≤r<4 B(r) = (10r + 3)\left(1 - \frac{1}{4}r\right)^{12}, \quad 0 \le r < 4 B(r)=(10r+3)(1−41r)12,0≤r<4Find the first four terms, in ascending powers of rrr, of the binomial expansion of
(1−14r)12 \left(1 - \frac{1}{4}r\right)^{12} (1−41r)12giving each term in simplest form.
Hence determine the coefficient of r3r^3r3 in the expansion of B(r)B(r)B(r), giving the answer in simplest form.
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.
