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1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 236
a.

Determine the first two terms, in ascending powers of uuu, of the binomial expansion of

(1+34u)−13 \left(1 + \frac{3}{4}u\right)^{-\frac{1}{3}} (1+43​u)−31​
[2]
b.

A signal processing engineer models the gain G G\,G of a circuit at frequency offset x x\,x using the formula:

G(x)=cos⁡(5x)+(1+6x2)−13 G(x) = \cos(5x) + \left(1 + 6x^2\right)^{-\frac{1}{3}} G(x)=cos(5x)+(1+6x2)−31​

Hence, for small values of xxx, show that the gain can be approximated by

G(x)≈A+Bx+Cx2 G(x) \approx A + Bx + Cx^2 G(x)≈A+Bx+Cx2

where AAA, B B\,B and C C\,C are constants to be found.

[4]
Markscheme

1.7 D: Sequences and series Questions

  1. A Level
  2. /Maths
  3. /1.7 D: Sequences and series

308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 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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