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1.6 Sequences and Series

1.6 Sequences and Series

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Question 228

The concentration of a specialized catalyst in a chemical reaction, CCC, is modeled by the function C(t)=(3+αt)4C(t) = (3 + \alpha t)^4C(t)=(3+αt)4 for small values of time t>0t > 0t>0, where α\alphaα is a non-zero constant.

a.

Given that the coefficient of the t2t^2t2 term in the binomial expansion of (3+αt)4(3 + \alpha t)^4(3+αt)4 is 135013501350, find the possible values of α\alphaα.

[3]
b.

A related adjusted concentration function, G(t)G(t)G(t), is defined by the product

G(t)=(127+2t3)(3+αt)4 G(t) = \left( \frac{1}{27} + \frac{2}{t^3} \right) (3 + \alpha t)^4 G(t)=(271​+t32​)(3+αt)4

Using your values from part (a), determine the possible values for the term independent of ttt in the binomial expansion of G(t)G(t)G(t).

[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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