A mathematical question

A man is initially standing at a certain point A. He starts walking 100 metres towards the east, then 50 metres towards the north, then 25 metres towards the west, then 12.5 metres towards the south, then 6.25 metres towards the east, then 3.125 metres (half of the previous distance) towards the north, and so on. Finally, He reaches a final point B after repeatedly walking in this fashion. What is the distance between points A and B?