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3 marksSequences

CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2 · Question 3(a)(i)

A sequence \{t_n\} is defined by the recurrence relation t_{n+1} = t_n + 5, t_1 = 11 for all n \in \mathbb{N}.

Determine t_2, t_3 and t_4.

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Other parts of this question

  1. 3(a)(ii)Express t_n in terms of n.[5 marks]
  2. 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]
  3. 3(c)(i)Express f(r) - f(r + 1) in terms of r.[3 marks]
  4. 3(c)(ii)Hence, or otherwise, find S_n = \sum_{r=1}^n \frac{4}{(r + 1)(r + 2)}.[4 marks]
  5. 3(c)(iii)Deduce the sum to infinity of the series in (c)(ii) above.[2 marks]

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