 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-1/4e/c/solution

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

(a_{n})

is bounded, apply Bolzano–Weierstrass to

(ℜ a_{n}, ℑ a_{n})

(or successively to both coordinates). If it is unbounded, recursively choose

n_{k} > n_{k - 1}

with

∣ a_{n_{k}} ∣ \geq k^{2}

. The alternatives are not exclusive:

0, 1, 0, 4, 0, 9, \dots

has both kinds of subsequence.

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