Okay, what the limit comparison test says is that if

and

are series of positive terms,

exists and

converges, then

converges. (The test is sometimes stated in the form that if the limit exists

__and is nonzero__ then

converges

__if and only if__ converges, but that is not what is needed for this example.)

If

, and you choose

for some p between and 2, then

will converge (because p>1), and

will be 0 (because p<2).

I hope that makes it clearer. (If you get an infraction for bumping, tell the Moderator that I think you were justified on this occasion.)