Find the binomial expansion of (2−3x)−1(2 - 3x)^{-1}(2−3x)−1 up to and including the term in x2x^2x2, giving each coefficient in its simplest form.
Show that the first three terms of this expansion form a geometric sequence, and state the common ratio.
State, using set notation, the range of values of x x\,x for which the expansion is valid.
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.