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3 marksSequences

CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2 · Question 4(a)(iii)a)

Given that a_n < 2 for all n,

Show that a_{n+1} < 2.

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Other parts of this question

  1. 4(a)(i)Find a_2 and a_3.[2 marks]
  2. 4(a)(ii)Express a_{n+1} - 2 in terms of a_n.[2 marks]
  3. 4(a)(iii)b)Show that a_n < a_{n+1}.[6 marks]
  4. 4(b)Find the term independent of x in the binomial expansion of (x^2 - \frac{6}{x^3})^{15}. [You may leave your answer in the form of factorials and powers,…[6 marks]
  5. 4(c)Use the binomial theorem to find the difference between 2^{10} and (2.002)^{10} correct to 5 decimal places.[6 marks]

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