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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/2011/paper-1/10/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 / 2011 / Paper 1 / 10 / b / Solution by

Codex  0 2026-10-18

Since

(1/2)^{3 k} = (1/8)^{k}

, this is a geometric series of first term

1

and common ratio

1/8

. Its sum is

\frac{1}{1 - 1/8} = \frac{8}{7} .

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