A signal processor's response function R(x)R(x)R(x) is defined by the expansion of R(x)=(2x−5)8R(x) = (2x - 5)^8R(x)=(2x−5)8.
Show that the first three terms, in descending powers of xxx, of this expansion are given by
256x8+ax7+bx6 256x^8 + ax^7 + bx^6 256x8+ax7+bx6where aaa and bbb are integers to be found.
Find the constant term in the expansion of
(2x−5x)8 \left(2x - \frac{5}{x}\right)^8 (2x−x5)8308 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.