Consider all points $(m,n)$ where $m$ and $n$ are natural numbers, $m\leq10$, and $n\leq5$. What is the average distances from each point to the origin $(0,0)$?
I know how to find the distance $d$ between the points $(x_1,y_1)$ and $(x_2,y_2)$; $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$.
In this case, the first point is $(m,n)$ and the second point is the origin, therefore the distance, $d=\sqrt{m^2+n^2}$.
It is annoying to find all distances, summing them, and dividing them by the number of distances, is not it annoying?
What if the given conditions, $m\leq10$ and $n\leq5$, were changed to $m\leq49$ and $n\leq36$?!