In the binomial expansion of (1+bx)n(1 + bx)^n(1+bx)n, where n n\,n is a rational number and b b\,b is a positive constant, the coefficient of x x\,x is 6 and the coefficient of x2 x^2\,x2 is -18.
Show that n=12\displaystyle n = \frac{1}{2}n=21 and find the value of bbb.
State, using set notation, the range of values of x x\,x for which the expansion is valid.
Find the coefficient of x3 x^3\,x3 in the expansion.
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.