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.
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.
