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CAPE Pure Mathematics Unit 2 · May/June 2021 · Paper 2 · Question 3(a)(ii)

A series is given as Σ (from k=1 to n) 8 / (4k² - 1).

Show that Σ (from k=1 to n) 8 / (4k² - 1) = 8n / (2n + 1).

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Other parts of this question

  1. 3(a)(i)Determine the THIRD partial sum, S₃, of the series.[3 marks]
  2. 3(b)(i)Determine the Taylor series expansion of e^(cos x) about x = π/2 up to the term in x³.[8 marks]
  3. 3(b)(ii)Use the series expansion to approximate e^(cos π) correct to 2 decimal places.[3 marks]
  4. 3(c)The first and fifth terms of a geometric progression are 16 and 9, respectively. Determine the THIRD term of the progression.[4 marks]

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