The sensitivity of a signal processor, S(x)S(x)S(x), is modeled by the function
S(x)=(2x−1.5)10 S(x) = (2x - 1.5)^{10} S(x)=(2x−1.5)10Show that the first three terms, in descending powers of xxx, of the expansion of S(x)S(x)S(x) are given by
1024x10+ax9+bx8 1024x^{10} + ax^9 + bx^8 1024x10+ax9+bx8where aaa and bbb are integers to be found.
In a modified design, the processor response is governed by the expansion of
(2x−32x)10 \left(2x - \frac{3}{2x}\right)^{10} (2x−2x3)10Find the constant term in this expansion.
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.
