You can't use lim n-> infinity = 0 as proof of convergence, right? If you could, that would mean 1/n converges, while we all know it diverges.
Asking because my book used it to show that sin(n^(1/2)) / n^(1/2) converged. If anybody could explain the proper way to do it, I'd be much obliged.
EDIT: I realize that's hard to read. This should make it a bit easier:
http://img218.imageshack.us/img218/6250/calccs2.png