The thought experiment goes like this:
Say there is some circuit which turns a lamp on/off with just a flick of a switch. Say its off; you flick it, it turns on; flick it again it turns off, and so on.
So say you are conducting the experiment for two minutes. When the remaining time halves, you flick the switch; and when that remaining time halves, you flick again...This process goes on infinitely, until two minutes is reached.
Mathematics says that the sum of all those remaining half-times will eventually tend to two minutes. And the outcome i.e. the final state is always unpredictable. We can't really know if its on/off.
Lets not concern about the final state. What would we actually observe towards the end, few micro seconds towards the two minute mark? Wouldn't the lamp appear turned on? What would happen if the time between two flicks tend to zero?