please help with x,y math question?

Question

An ant of negligible dimensions starts at the origin (0,0) of the standard twodimensional
rectangular coordinate system. The ant walks one unit right, then onehalf
unit up, then
1/4 unit left, then 1/8 unit down, etc. In each move, it always turns counterclockwise
at
a 90 degree angle and goes half the distance it went on the previous move. Which point
(x,y) in the xyplane
is the ant approaching in its spiraling journey?

Answer 1

x = 1 - 1/4 + 1/4^2 - 1/4^3 + . . . . .
x = (1 + (1/4)^n) / (1 + 1/4)
lim (x) = 4/5 = 0.8
n→∞

y = (1/2)(4/5) = 2/5 = 0.4

(x,y) = (0.8,0.4)