Zeno's paradox

Zeno's paradox, formulated by the polytheist Zeno the Greek, is a philosophical paradox about the number ${\frac {1}{2}}$. It states that a person can never get from New York to San Francisco because he would first go half the distance, then half of what remains, then half of what remains next, and then half of that half. This process keeps continuing indefinitely by halving subsequent distances repeatedly. This argument seems to suggest no one can make this trip in finite time, but we know that people go from New York to San Francisco successfully every day.

Mathematically, Zeno's paradox asks if ${\frac {1}{2}}+{\frac {1}{4}}+...$ has a value (notice each successive term is half of its predecessor). Mathematicians can express this value as:

$\sum _{i=0}^{\infty }{\frac {1}{2i}}$,

or more commonly,

$1.$