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2 marksSequences

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

The sequence \{a_n\} of positive numbers is defined by a_{n+1} = \frac{4(1 + a_n)}{4 + a_n}, a_1 = \frac{3}{2}.

Find a_2 and a_3.

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Other parts of this question

  1. 4(a)(ii)Express a_{n+1} - 2 in terms of a_n.[2 marks]
  2. 4(a)(iii)a)Show that a_{n+1} < 2.[3 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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