 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/26l/d/solution

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

Again the series converges absolutely.

T = 2 \sum_{j} B_{j} / 3^{j}

has the Cantor distribution. Every particular digit sequence has probability zero, so it has no atoms; its support is the Cantor set, which has Lebesgue measure zero, so it cannot have a Lebesgue density.

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