Let $X_1,X_2,...$ independent random variables, with $P(X_n=n)=1/{n^2}$ and $P(X_n=1/n)=1-1/{n^2}$ . Show that $X_n\to0$ in probability.
I got this problem in an old probability test but I'm not sure how to use the definition of convergence in probability:
$X_n\to X$ in probability, if $P(\omega \in \Omega | \lim_{n\to \infty}X_n(\omega))=1$
p.s.: I'm using Sheldon Ross' book "A First Course in Probability", but it doesn't have a convergece topic. Is there a better book?