Take your thumb and your forefinger and spread them apart as far as possible. This represents a distance. Now make that distance one half as large. Continue to cut the distance between them in half.
This is a version of the Zeno paradox!
About Achilles, and the arrow never reaching the target.
It was the root of millennial discussions.

The answer satisfying me is that there is un underlying problem about time: are you making each move in the same time, say a second?In that case, yes, they never touch.

But the model of real motion is such that you are making every step in a time that is half of the previous time.

So now they will touch, and this corresponds to the fact that
1 + 1/2 + 1/4 + 1/8 + ... is equal to 1
The meaning of the infinite sum above is the limit of the partial sums of the first n terms, as n is infinitely growing (same subject as in 0.999....=1 question)