The difference between a convergent and a divergent series is almost the difference between being or not being.

If someone would give one half of dollar one week and later the half other week and the half of the have every week. I would never be rich because the final quantity of money I would have might be  1 dollar. (Converge)

But if someone gave a dollar the first week and the double after and after I would probably be rich because after several years I would have a lot of money.

The difference between being rich or not