A chemical engineer is modeling the yield, YYY, of a reaction as a function of the catalyst concentration, ccc. The relationship is given by the formula:
Y(c)=1+6c23∣c∣<16 Y(c) = \sqrt[3]{1 + 6c^2} \quad \quad |c| < \frac{1}{\sqrt{6}} Y(c)=31+6c2∣c∣<61Find, in ascending powers of ccc, the first three non-zero terms of the binomial series expansion of Y(c)Y(c)Y(c), giving each coefficient as a simplified fraction.
Use the expansion from part (a) with c=13c = \frac{1}{3}c=31 to find a rational approximation to k⋅53k \cdot \sqrt[3]{5}k⋅35, where kkk is a constant you must determine.
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.