 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/7/a/solution

1/2

and argument

- 3 x

(1 - 3 x)^{1/2} = 1 + \frac{1}{2} (- 3 x) + \frac{( 1/2 ) ( - 1/2 )}{2 !} (- 3 x)^{2} + O (x^{3}) .

Thus the first three nonzero terms are

1 - \frac{3}{2} x - \frac{9}{8} x^{2} + O (x^{3}) .

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