>**Problem.** Is the series $$\sum_{n=1}^\infty\frac{|\sin(n)|^n}n$$convergent?

(The problem was posed on 22.06.2017 by Ph D students of H.Steinhaus Center of Wroclaw Polytechnica. The promised prize for solution is  "butelka miodu pitnego", see page [37][1] of [Volume 1][2] of the [Lviv Scottish Book][3].
To get the prize, write to the e-mail: [email protected]).


  [1]: http://www.math.lviv.ua/szkocka/viewpage.php?vol=1&page=37
  [2]: http://www.math.lviv.ua/szkocka/viewbook.php?vol=1
  [3]: http://www.math.lviv.ua/szkocka