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 (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.