I have a homework problem that I arrived.
With Mathematica, the limit is 0. So by using $\epsilon= 10^{-6}$ (it is -6, not -0, sorry for the cutoff).
$\sin(n^2)/\sqrt{n} <\epsilon =10^{-6}$
So I tried putting that ino Mathematica and no luck so I have a feeling I am approaching this problem the wrong way