 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/iii/solution

The elementary bound

∣ sin t ∣ \leq ∣ t ∣

gives

0 \leq sin^{2} (1/ n) \leq 1/ n^{2}

. Comparison with a convergent p-series proves the series converges.

 New to topics? Read the docs here!