Let A (a, b) be a fixed point and O be the origin of  coordinates, If A1 is the mid-point of OA, A2 is the mid-point of -.A1, A3 is the mid-point of AA2 and so on. Then the coordinates of A1  are

The coordinates of A1 are a2,b2the coordinates of A2 are a+a22,b+b22=a2+a22,b2+b22the coordinates of A3 are a+a2+a222,b+b2+b222=a2+a22+a23,b2+b22+b23Continuing in this manner we observe that the coordinates of A1 area2+a22+a23+……+a2n,b2+b22+b23+….+b2n=a1−12n,b1−12n=a1−2−n,b1−2−n