 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/10/a/solution

Pair the first and last terms of the arithmetic series. There are

500

pairs, each summing to

1001

, so

N_{1} = \frac{1000 \cdot 1001}{2} = 500 500.

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