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 Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 115 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, matched to the Edexcel A Level Maths (9MA0) 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.
