Corollary 2

If the infinite product with general factor $x_n$ is convergent, and if $\prod_{n=0}^\infty x_n$ is a unit, then the infinite product with general factor

is convergent.

The product of the sequence $(y_n)$ is denoted by $\prod_{n=h}^\infty x_n$, and is also called the residue of index $h$ of the infinite product with general factor $x_n$.

Still under the assumption that $\prod_{n=h}^\infty x_n$ is a unit, it follows from Proposition 2 that if $(z_n)$ is a sequence such that $z_n = x_n$ for all but a finite number of indices, then the product with general factor $z_n$ is convergent.