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5 marksSeries

CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2 · Question 3(b)(i)

The sum of the first n terms of a series, S, is 9 - 3^{2-n}.

Find the n-th term of S.

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Other parts of this question

  1. 3(a)Prove by Mathematical Induction that u_n = n! for all n \in \mathbb{N}.[9 marks]
  2. 3(b)(ii)Show that S is a geometric progression.[2 marks]
  3. 3(b)(iii)Find the first term and common ratio of S.[2 marks]
  4. 3(b)(iv)Deduce the sum to infinity of S.[2 marks]

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