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.
