A quantitative analyst models the projected value of a portfolio using the function
V(x)=(4+kx)7V(x) = (4 + kx)^7V(x)=(4+kx)7
where x x\,x represents market volatility and k k\,k is a positive constant.
Find the first three terms, in ascending powers of xxx, in the expansion of (4+kx)7(4 + kx)^7(4+kx)7, giving each term in its simplest form.
Given that the coefficient of x2 x^2\,x2 is exactly three-eighths of the coefficient of xxx, determine the value of kkk.
200 exam-style questions on CCEA A Level Maths 3.3 Sequences and series (A-level only), covering 3.3.1 Sequences and series (A-level only), 3.3.2 Sequences and series (A-level only), 3.3.3 Sequences and series (A-level only), 3.3.4 Sequences and series (A-level only), 3.3.5 Sequences and series (A-level only), 3.3.6 Sequences and series (A-level only), 3.3.7 Sequences and series (A-level only), and 3.3.8 Sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.