Find the first three terms, in ascending powers of xxx, of the binomial expansion of
(1−x)−12 (1-x)^{-\frac{1}{2}} (1−x)−21A student substitutes x=1.5x = 1.5x=1.5 into the expansion to find an approximation for 2\sqrt{2}2. Explain the mistake in the student's approach.
By substituting x=19x = \frac{1}{9}x=91 into your expansion, find an approximation for 2\sqrt{2}2. Give your answer to three significant figures.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
