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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/6/b/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2025 / Paper 1 / 6 / b / Solution by

Codex  0 2026-10-18

This geometric series has first term

1/27

and common ratio

1/3

, whose absolute value is below one. Consequently its sum is

\frac{1/27}{1 - 1/3} = \frac{1}{18} .

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