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.
200 exam-style questions on CCEA A Level Maths 3.3 Sequences and series (A-level only), covering 3.3.1 Sequences and series (A-level only), 3.3.2 Sequences and series (A-level only), 3.3.3 Sequences and series (A-level only), 3.3.4 Sequences and series (A-level only), 3.3.5 Sequences and series (A-level only), 3.3.6 Sequences and series (A-level only), 3.3.7 Sequences and series (A-level only), and 3.3.8 Sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.