Just like the title, is there a subsequence of $(\sin(n))_{n \in \mathbb{N}}$ that converge to 1 ? If it is, how to prove it? If it's possible, how to construct this subsequence? If it is not exist, how to prove it?
Is there a subsequence of (sin(n)) that converge to 1?
0
$\begingroup$
sequences-and-series
-
0Is $1$ a limit point of set $X=\{sin(n)\}$? – 2017-02-27
-
0I'm pretty sure that $\{sin(n)\}$ is dense in $(-1,1)$. Edit: Yes, see http://math.stackexchange.com/questions/4764/sine-function-dense-in-1-1 – 2017-02-27