The expression (1+3x)−2(1 + 3x)^{-2}(1+3x)−2 is expanded as a binomial series in ascending powers of xxx.
State the range of values of x x\,x for which the expansion is valid.
Select the correct answer.
∣x∣<13|x| < \frac{1}{3}∣x∣<31
∣x∣<12|x| < \frac{1}{2}∣x∣<21
∣x∣<2|x| < 2∣x∣<2
∣x∣<3|x| < 3∣x∣<3
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.