Given that kkk is a constant and the binomial expansion of
1+kx,∣kx∣<1 \sqrt{1 + kx}, \quad |kx| < 1 1+kx,∣kx∣<1in ascending powers of xxx up to the term in x3x^3x3 is
1+14x+Ax2+Bx3 1 + \frac{1}{4}x + Ax^2 + Bx^3 1+41x+Ax2+Bx3(i) find the value of kkk,
(ii) find the value of the constant AAA and the constant BBB.
Use the expansion to find an approximate value to 1.2\sqrt{1.2}1.2.
Show your working and give your answer to 6 decimal places.
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.
