Originally Posted by

**arbolis** Oh... As n tends to $\displaystyle \infty$, the sum I made is in fact lim $\displaystyle n*\frac{1}{n}$ as tends to $\displaystyle +\infty$. So of course it's always equal to $\displaystyle 1$. 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 $\displaystyle \frac{1}{+\infty}$) 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?"