The function f f\,f is given by
f(x)=1+axf(x) = \sqrt{1 + ax}f(x)=1+ax
where a a\,a is a non-zero constant.
In the binomial expansion of f(x)f(x)f(x), the coefficients of x x\,x and x2 x^2\,x2 are equal.
Find the value of aaa.
Using this value of aaa, state, using set notation, the values of x x\,x for which the binomial expansion is valid.
Using this value of aaa, write down the quadratic function that approximates f(x)f(x)f(x) when x x\,x is small.
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, 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). Each one has a worked solution and a mark scheme showing where the marks go.