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Binomial Expansion

Binomial Expansion

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Question 306
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.

Hence, in a signal processing application, for small phase offsets θ\thetaθ, show that the windowing function W(θ)W(\theta)W(θ) defined by

W(θ)=cos⁡(5θ)+(1−32θ2)−13 W(\theta) = \cos(5\theta) + \left(1 - \frac{3}{2}\theta^2\right)^{-\frac{1}{3}} W(θ)=cos(5θ)+(1−23​θ2)−31​

can be approximated by A+Bθ+Cθ2A + B\theta + C\theta^2A+Bθ+Cθ2, where AAA, BBB and CCC are constants to be found.

[4]
Markscheme

Binomial Expansion Questions

  1. A Level
  2. /Maths
  3. /Binomial Expansion

408 exam-style questions on Edexcel A Level Maths Binomial Expansion, covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions. Each one has a worked solution and a mark scheme showing where the marks go.

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