 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/10/b/solution

The finite geometric series has eleven terms, from

2^{1}

through

2^{11}

2

N_{2} = 2 \frac{2 ^{11} - 1}{2 - 1} = 4094.

Counting the powers explicitly avoids omitting the final

2048

term.

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