Endgame

The endgame in mindsport was:
A man is initially standing at a certain point A. He starts walking 100 meters towards the east, then 50 meters towards the north, then 25 meters towards the west, then 12.5 meters towards the south (half the previous distance) and so on. He reaches a point B finally after repeatedly walking in this fashion. What is the distance between points A and B?

The answer that showed up was:
[take this as a paragraph of extremely complicated mathematics, and you do not really need to read it for the purpose of this post]

100*[2/sqrt(5)] = 89.443 meters. It’s the sum of two series (since going east initially) 1-1/4+1/16-1/64+… = 4/5. The X co-ordinate is the negative term of the series (since going north at first turn) ½*[1-1/4+1/16-1/64+…=2/5. by simple distance formula, assuming man was initially at origin: Dist = sqrt[(2/5)]-2+(4/5)-2=2/sqrt(5)*100=89.443 m.

Frankly speaking, I neither had the inclination nor the brains to get past the first time the word “co-ordinate” appears. However, I hit upon a pretty close answer of 89.445 meters by plotting the movement on a sheet of graph paper at 1/10th the scale. And, the answer that he has given is also not the ACCURATE answer, it’s just more accurate than mine by 0.002.