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 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.