5 marksThe Binomial Theorem
CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2 · Question 4(a)(i)
Find n \in \mathbb{N} such that 5\binom{n}{2} = 2\binom{n+2}{2}.
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Practise this questionOther parts of this question
- 4(a)(ii)The coefficient of
x^2in the expansion of(1 + 2x)^5 (1 + px)^4is-26. Find the possible values of the real numberp.[7 marks] - 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 ofxfor which the series is valid.[2 marks] - 4(b)(ii)Use Maclaurin's theorem to obtain the first THREE non-zero terms in the power series expansion in
xof\sin 2x.[7 marks] - 4(b)(iii)Hence, or otherwise, obtain the first THREE non-zero terms in the power series expansion in
xof\ln(1 + \sin 2x).[4 marks]
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