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.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.