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.
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, 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). Each one has a worked solution and a mark scheme showing where the marks go.