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.
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.