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7 marksThe Binomial Theorem

CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2 · Question 4(a)(ii)

The coefficient of x^2 in the expansion of (1 + 2x)^5 (1 + px)^4 is -26. Find the possible values of the real number p.

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Other parts of this question

  1. 4(a)(i)Find n \in \mathbb{N} such that 5\binom{n}{2} = 2\binom{n+2}{2}.[5 marks]
  2. 4(b)(i)Write down the first FOUR non-zero terms of the power series expansion of \ln(1 + 2x), stating the range of values of x for which the series is valid.[2 marks]
  3. 4(b)(ii)Use Maclaurin's theorem to obtain the first THREE non-zero terms in the power series expansion in x of \sin 2x.[7 marks]
  4. 4(b)(iii)Hence, or otherwise, obtain the first THREE non-zero terms in the power series expansion in x of \ln(1 + \sin 2x).[4 marks]

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