So I am getting ready for my first econometrics exam, and we have a lot of these plim (probability limits). Looking at the definition, I have that as n goes to infinity, $$P(|X_n-Q|>\epsilon)\rightarrow0 $$ And then there are a couple of theorems I get, including plim(A+B), plim(AB), but these require I know what plim(A) and plim(B) are. One simple example that I did not understand was: $$\frac{1}{n}plim(\sum X_i^2)$$ I thought that it would go to 0 in the limit that n gets really large.
What is the proper way to approach this?