 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2011/ia/paper-1/3f/b/solution

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

Take

a_{n} = n

. Every subsequence has the form

a_{n_{k}} = n_{k}

, with

n_{k} \geq k

, so it tends to positive infinity and cannot converge to a real number. Thus this sequence has no convergent subsequence.

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