 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/6/a/solution

Group consecutive terms in pairs. The

j

th pair, for

j = 1, \dots, 25

, is

- \frac{4 j - 3}{2} + \frac{4 j - 1}{2} = 1.

There are

25

such pairs in this finite sum, so the answer is

25

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