Oh... As n tends to

, the sum I made is in fact lim

as tends to

. So of course it's always equal to

. Nice problem! You can try to ask to someone that knows a bit of probability : "Explain me how this could be : if there are an infinity of radius in a circle and I want to chose exactly one. There is a probability of 0 (well

) to pick up one in particular. Repeating this with "all" the radius, none of them have a probability to get chosen greater than 0. So how can you explain that I will chose one of them?"