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.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.