An example of converge in probability but not almost sure converge

This is one homework question in stochastic process class. I cannot come up even one example by myself. First I use goole, nothing valuable is found. Then I http://books.google.com/. I get a book named 'Counterexamples in Probability and Statistics'. The example is X_n=H_n, where H_n is Bernoulli variable with probability 1/n to be 1. X_n converge to 1 in probability. But Prob(H_n = 1 infinity often)=1 by Borel Cantelli Lemma.