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4 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2007 · Paper 2 · Question 2(a)

Let S_n = Σr for n ∈ N.

Find the value of n for which 3S_{2n} = 11 S_n. Note: Σr = n(n+1)/2.

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Other parts of this question

  1. 2(b)(i)Express p and q in terms of α and β.[2 marks]
  2. 2(b)(ii)Find the values of α and β.[4 marks]
  3. 2(b)(iii)Hence, determine the values of p and q.[2 marks]
  4. 2(c)Prove, by Mathematical Induction, that n^2 > 2n for all integers n ≥ 3.[8 marks]

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