The following sum is (wrongly) obtained by trying a variation on Zeno's arrow paradox :
$$\left(1-\frac12\right) + \left(1-\frac12\right)\frac13+ \left(1-\frac12\right)\left(1-\frac13\right)\frac14+ \left(1-\frac12\right)\left(1-\frac13\right)\left(1-\frac14\right)\frac15+\cdots$$
With following variation on Zeno's original problem : An arrow travelling between $0$ and $1$ , after travelling $\frac12$ distance, it will travel the $\frac13$ of remaining distance, after that $\frac14$ of the remaining distance, after that $\frac15$ of the remaining distance, and so on and so forth.
from the formulation this series has to converge to a value less than $\frac34$ .
My question is there a closed form known for this ? ( is the above sum correct formulation of the described problem ? No it does NOT)