Mathematics

Mathematics

Problem

Show that the series ∑n=1∞sin⁡ ⁣(1n)\displaystyle\sum_{n=1}^{\infty}\sin\!\left(\frac{1}{n}\right) diverges. Provide inequalities giving both an upper and a lower bound for sin⁡ ⁣(1n)\sin\!\left(\frac{1}{n}\right) that enable a direct comparison with a pp-series, then state your conclusion.

Browse the problem library