I suspect that you are confusing a sequence, {a_{n}}, with a series, [itex]\sum a_n[/itex]. If lim a_{n} = 0 (or any specific number), the sequence converges, but nothing can be said about the series [itex]\sum a_n[/itex].I thought what I did was a test?? Ahhh this stuff is so confusing! So many times in my book it said if the lim of an=0, then it converges. I dont get whats going on.