Phil Reconstruct the Zenos Achilles vs Tortoise argument P1

Phil:

Reconstruct the Zeno\'s Achilles vs. Tortoise argument (P₁, P₂, P₃, C)

http://platonicrealms.com/encyclopedia/zenos-paradox-of-the-tortoise-and-achilles

Solution

Zeno\'s Achilles vs. Tortoise argument states that if the tortoise covers a distance x then the Achilles needs to cover it to reach him..so everytime it tries to catches the tortoise and the tortoise moves a little further however small it may be.
It can be explained better by one more example given in the article..the case where the person covers half the distance every time he moves.
So the case is like = 1+1/2+1/4+1/8+1/16 upto infinite terms.
So you may think it equals to infinity but the case is not so.
It is a progression with a common ratio which is added upto infinity.
And can be calculated easily by S=a/(1-r) where a is the first term and r is the common ration.
So in the above progression a=1, r=1/2 so the sum is 1/(1-1/2)=2. So while following the similar pattern he covers the entire distance.