Find the first 4 terms, in ascending powers of xxx, of the binomial expansion of
(3+kx9)6 \left(3 + \frac{kx}{9}\right)^6 (3+9kx)6where kkk is a non-zero constant. Give each term in its simplest form.
Given that
f(x)=(4+2x)(3+kx9)6 f(x) = (4 + 2x)\left(3 + \frac{kx}{9}\right)^6 f(x)=(4+2x)(3+9kx)6and that in the expansion of f(x)f(x)f(x), the coefficient of xxx is equal to the constant term, find the value of kkk.
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.