Given the series:
$\sum_{n=1}^\infty \frac{1}{\sin n};$
does it converge? I think not but I believe that I saw somewhere in a book that it does? .... or maybe that was $\displaystyle\sum\limits_{n=1}^\infty \frac{1}{{\sin n}^2}$?
Edit: sorry, I meant $n$ .
Thanks!
Side question: Can you think of a series involving $\sin$ that supposedly gets smaller (closer to $y=0$) as it oscillates rapidly to infinity? I seem to remember reading something similar but cannot remember exactly what it was.