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 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.