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1.6 Sequences and Series

1.6 Sequences and Series

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Question 144

In a precision chemical synthesis, the concentration CCC, in moles per litre, of a specific reagent is modelled by the function C(x)=(12−4x)10C(x) = \left( \frac{1}{2} - 4x \right)^{10}C(x)=(21​−4x)10 for 0≤x<0.1250 \le x < 0.1250≤x<0.125, where xxx represents the mass in grams of a stabilizer added.

Determine the first four terms, in ascending powers of xxx, of the binomial expansion of C(x)C(x)C(x). Give each coefficient as a simplified fraction or an integer.

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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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