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CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2 · Question 3(a)(i)

SECTION B - Module 2

Prove, by mathematical induction, that for n \in \mathbb{N}, S_n = 1 + \frac{1}{2} + \frac{1}{2^2} + \frac{1}{2^3} + \dots + \frac{1}{2^{n-1}} = 2 - \frac{1}{2^{n-1}}.

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Other parts of this question

  1. 3(a)(ii)Hence, or otherwise, find \lim_{n \to \infty} S_n.[3 marks]
  2. 3(b)Find the Maclaurin expansion for f(x) = (1 + x)^2 \sin x up to and including the term in x^3.[14 marks]

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