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4 marksSeries

CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2 · Question 3(c)(ii)

Let f(r) = \frac{1}{r + 1}, r \in \mathbb{N}.

Hence, or otherwise, find S_n = \sum_{r=1}^n \frac{4}{(r + 1)(r + 2)}.

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Other parts of this question

  1. 3(a)(i)Determine t_2, t_3 and t_4.[3 marks]
  2. 3(a)(ii)Express t_n in terms of n.[5 marks]
  3. 3(b)Find the range of values of x for which the common ratio r of a convergent geometric series is \frac{2x - 3}{x + 4}.[8 marks]
  4. 3(c)(i)Express f(r) - f(r + 1) in terms of r.[3 marks]
  5. 3(c)(iii)Deduce the sum to infinity of the series in (c)(ii) above.[2 marks]

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