Let $k$ be a field and let $X_1, X_2, \ldots , X_n$ be formal noncommuting variables and let $K\langle \langle X_1, X_2, \ldots , X_n\rangle \rangle $ be the formal noncommutative power series ring in these variables.
Suppose $F$ is a power series in this ring such that its constant term is nonzero. How to prove that $F^{-1}$ exists?