 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-1/9e/d/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Write

\frac{j}{j ^{2} + j + 1} = \frac{1}{j} + O (j^{- 2})

uniformly for

j \geq 1

. The accumulated error from

j = n + 1

2 n

tends to zero, while the corresponding harmonic sum tends to

lo g 2

. Hence

b_{n} \to lo g 2

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