Question

An ant of negligible dimensions start at the origin (0,0) of the standard 2-dimensional rectangular coordinate system. The ant walks one unit right, then one-half unit up, then one-quarter unit left, then one-eighth unit down, etc. In each move, it always turn counter-clockwise at a 90 degree angle and goes half the distance it went on the previous move. Which point (x,y) in the xy-plane in the ant approaching in its spiraling journey?

Answer:
(4/5 , 2/5)

How do you get this answer? I'd really appreciate it if you explain me how to get that answer!

Thanks

Answer 1

Hint: Write the formula for its movements in the x direction only.

Also write the formula for its movements in the y direction.

Both of your equations will have limits.

Your coordinate solution will be the limits as the ant moves an infinite number of times.

Answer 2

Can you please explain how to do this question thoroughly? I don't know what you're talking about...