 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/7/b/solution

There are

N + 1

terms, namely

1, 2, \dots, N + 1

n = 0 \sum N (n + 1) = \frac{( N + 1 ) ( N + 2 )}{2}, N \in Z_{\geq 0} .

Pairing the first and last terms gives pair sum

N + 2

, explaining both factors.

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