## Probability distribution without a mean?

I don't see how this is possible? how can you have a distrubution with no mean?
My professor says there is, but i don't get it...
 Recognitions: Homework Help Science Advisor Exercise: find a series a_1+a_2+.... that has a finite sum (and hence is can be made to have sum 1, and be a prob distribution on N) but where a_1+2a_2+3a_3+... is not finite (so there isn't a mean). And there are less contrived examples too.
 Recognitions: Science Advisor Simple example a_k=1/k^2