A person standing at the center of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?

A

$$32/ \sqrt{5}$$ meters

B

$$64/ \sqrt{5}$$ meters

C

32 meters

D

64 meters