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 (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.