A sequence converges if the lim (as n-> infinity exists), and diverges if the lim is infinity, or DNE

also, tell him that when taking limits, if he happens to get 0/0, or infinity/infinity, he can do L'Hopital's rule to find the real limit (and also that, if he tries to find the limit and comes up with infinity times infinity, or 0 times 0, he can re-work them algebraically to be inf/inf, or 0/0. an example of this would be (x)ln(1 +1/x). normally this would be infinity times 0, but reworking it... ln(1 +1/x)/(1/x) = 0/0, and do L'Hopitals from there).