Expand (1+3x)−3(1 + 3x)^{-3}(1+3x)−3 in ascending powers of x x\,x up to and including the term in x3x^3x3.
Write down the range of values of x x\,x for which the expansion is valid.
Hence find the expansion of 2x+1(1+3x)3\dfrac{2x + 1}{(1 + 3x)^3}(1+3x)32x+1 up to and including the term in x3x^3x3.
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.