Question 1

Paper 2, calculatorMedium12 marks

Let SS be a set of 9 distinct elements. Let NN be the number of subsets of SS that contain exactly 4 elements, and define

k=(1+1N)1/2.k=\left(1+\frac{1}{N}\right)^{1/2}.
(a)

Determine NN

[2]
(b)

Find the first four non-zero terms, in descending powers of NN in the binomial expansion of kk

[4]
(c)

Hence use the first three non-zero terms of this expansion to estimate kk Give your answer to 9 significant figures.

[2]
(d)

Use your GDC to determine kk and hence find the absolute difference between this value and your estimate in part (c), correct to 2 significant figures.

[3]
(e)

State whether your estimate in part (c) gives kk correctly to 3 decimal places.

[1]

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