 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/7/a/solution

1

0.999

, which lies strictly inside the unit interval. Therefore

n = 0 \sum \infty (0.999)^{n} = \frac{1}{1 - 0.999} = 1000.

The decimal is treated as the exact value

999/1000

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