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 (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.