 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/8/a/solution

2^{- 4} = 1/16

1/2

, whose absolute value is less than one. Consequently

n = 4 \sum \infty 2^{- n} = \frac{1/16}{1 - 1/2} = \frac{1}{8} .

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