I want to know about the convergence or divergence of the following series:
$$\sum \sin (a_n) $$
The tests that I tried were inconclusive. Is it possible to know?
Or, more generally, does this series converge for all conditionally convergent series given by the sequence $a_n$? I know this result holds for any absolutely convergent series (here), but I want to know if it works for any convergent series or if there's an explicit counterexample taking conditionally convergent series.
EDIT: as pointed out at the answer section, my example converges, but the general case is still unanswered.