Here is a series, a friend of mine gave me.
Examine the convergence of the series $$\sum_{n=1}^{\infty}\frac{\sin(\sqrt{n})}{n}.$$ It is from the book A Garden of Integrals, Frank E. Burk. It is given after the chapter "The Euler Summation Formula". So I am interested in a solution, which avoids this formula, and is, say, more elementary in terms of the tools it uses. Thank you!
EDIT. Thanks for pointing out the earlier question. Sorry that I did not look up. The solution there is very nice. If you find any other solutions, please post them.
