 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/2/i/solution

For

n \geq 1

ln n \leq n

and

2 n^{3} + 1 \geq 2 n^{3}

. Hence

0 \leq ln n / (2 n^{3} + 1) \leq 1/ (2 n^{2})

. The comparison p-series has exponent two and converges, so the series converges by the comparison test.

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