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1.6 Sequences and Series

1.6 Sequences and Series

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Question 135

The reaction rate R R\,R of a biochemical catalyst depends on its concentration ccc (in mol dm−3^{-3}−3) according to the model

R(c)=1+8c23,∣c∣<18 R(c) = \sqrt[3]{1 + 8c^2}, \quad |c| < \frac{1}{\sqrt{8}} R(c)=31+8c2​,∣c∣<8​1​
a.

Find, in ascending powers of ccc, the first three non-zero terms of the binomial series expansion of R(c)R(c)R(c), giving each coefficient as a simplified fraction.

[4]
b.

By substituting c=14\displaystyle c = \frac{1}{4}c=41​ into the expansion from part (a), find a rational approximation to k33k \sqrt[3]{3}k33​, where k k\,k is a constant you must determine.

[4]
Markscheme

1.6 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.6 Sequences and Series

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.

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