 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-1/7/a/solution

(1 + 0.01)^{9} = 1 + 9 (0.01) + 36 (0.01)^{2} + 84 (0.01)^{3} + 126 (0.01)^{4} + \dots = 1.093685272 \dots .

Thus, to three decimal places,

(1.01)^{9} ≃ 1.094.

The first three nonconstant terms already determine this rounding; the remaining positive terms total less than

1.3 \times 1 0^{- 6}

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