In this question you should assume that −12<x<12\displaystyle -\frac{1}{2} < x < \frac{1}{2}−21<x<21.
For the binomial expansion of (1−2x)−2(1 - 2x)^{-2}(1−2x)−2, find and simplify the first four terms.
Write down the sum to infinity of the series 1+2x+4x2+8x3+…1 + 2x + 4x^2 + 8x^3 + \dots1+2x+4x2+8x3+…
Hence, or otherwise, find and simplify an expression for 2+6x+16x2+40x3+…2 + 6x + 16x^2 + 40x^3 + \dots2+6x+16x2+40x3+…
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.