3 marksThe Binomial Theorem
CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2 · Question 4(a)(ii)b)
Hence, obtain an estimate for (1.01)^{10}.
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Practise this questionOther parts of this question
- 4(a)(i)For the binomial expansion of
(2x + 3)^{20}, show that the ratio of the term inx^6to the term inx^7is\frac{3}{4x}.[5 marks] - 4(a)(ii)a)Determine the FIRST THREE terms of the binomial expansion of
(1 + 2x)^{10}.[4 marks] - 4(b)Show that
\frac{n!}{(n - r)!r!} + \frac{n!}{(n - r + 1)!(r - 1)!} = \frac{(n + 1)!}{(n - r + 1)!r!}.[6 marks] - 4(c)(i)Show that the function
f(x) = -x^3 + 3x + 4has a root in the interval[1, 3].[3 marks] - 4(c)(ii)By taking
x_1 = 2.1as a first approximation of the root in the interval[1, 3], use the Newton–Raphson method to obtain a second approximation,x_2, in…[4 marks]
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