 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2009/ia/paper-1/3f/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

Rationalizing avoids cancellation between the two large terms of the sequence:

a_{n} = \frac{n}{n + n ^{2} - n} = \frac{1}{1 + 1 - 1/ n} .

By continuity of the square root and the reciprocal at the limiting values,

n \to \infty lim a_{n} = \frac{1}{2} .

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