 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/19/c/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

Here

∣ a_{n + 1} / a_{n} ∣ = n / (n + 1) \to 1

. Therefore the ratio test is inconclusive. The series does in fact converge by the alternating series test, and fails to converge absolutely because the harmonic series diverges; these facts use other tests.

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