For what values of $k>1$ does $\sum_{n>1} 1/(n^k\sin(n))$ converge?
Asked
Active
Viewed 89 times
0
-
That depends on the irrationality measure of $\pi$ and I believe is an open problem. – Jack D'Aurizio Jul 22 '16 at 15:50
-
Due to the work of Viola and Rhin, it is convergent for any $k\geq 8$, but that is probably very far from being the optimal bound. – Jack D'Aurizio Jul 22 '16 at 15:51
-
Related: http://math.stackexchange.com/questions/20555/are-there-any-series-whose-convergence-is-unknown – Jack D'Aurizio Jul 22 '16 at 17:39