 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1/19/b/i/solution

The term at

k = 0

is finite. For every

k \geq 1

0 < \frac{1}{1 + k ^{2}} \leq \frac{1}{k ^{2}} .

The comparison P-series

\sum k^{- 2}

converges, so the comparison test for series proves that the given series converges absolutely.

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