We show that every formal embedding sending a real-analytic strongly
pseudoconvex hypersurface in M\subset \C^N into another such hypersurface in
M'\subset \C^{N+1} is convergent. More generally, if M and M′ are merely
Levi-nondegenerate, the same conclusion holds for any formal embedding provided
either that the embedding is CR transversal or the target hypersurface does not
contain any complex curves.Comment: 8 page