Find, in ascending powers of xxx, the first three non-zero terms of the binomial series expansion of
1+3x23∣x∣<13 \sqrt[3]{1 + 3x^2} \quad \quad |x| < \frac{1}{\sqrt{3}} 31+3x2∣x∣<31giving each coefficient as a simplified fraction.
Use the expansion from part (a) with x=12x = \frac{1}{2}x=21 to find a rational approximation to k⋅73k \cdot \sqrt[3]{7}k⋅37, where kkk is a constant you must determine.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
