1. The problem statement, all variables and given/known data Determine whether the following sequence, whose nth term is given, converges or diverges. Find the limit of each convergent one. n[1 - cos(2/n)] 2. Relevant equations I have made a solid attempt and obtained an answer but I am convinced I made a mistake and have missed something. 3. The attempt at a solution lim n[1 - cos(2/n)] lim [ n - n[cos(2/n)] ] lim(n) - lim (n[cos(2/n)]) lim(n) - lim ( [cos(2/n)] / (1/n) ) <--- Now using L'Hopital's Theorem: lim(n) - lim ( [(-2/n^2)sin(2/n)] / (-1/n^2) ) lim(n) - lim 2sin(2/n) lim(n) - 2sin(lim [2/n]) Infinity - 0 = Infinity, hence divergent! Note: Each limit (lim) shown about is the limit as n approaches infinity, just didn't write it every time to make things a bit neater. Now for some reason that seems to simple and incorrect to me. Confirmation or any sort of help would be much appreciated. Sorry about the confusing working above, thanks guys.