Corollary 2

If the infinite product of general factor $x_n$ is convergent, and if $\prod_{n=0}^\infty x_n$ is invertible, the infinite product of general factor $y_n = x_{n+h} (n \geq 0)$ is convergent.

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

Assuming still that $\prod_{n=0}^{\infty} x_n$ is invertible, we deduce also from prop. 2 (IX, p. 82) that, if $(z_n)$ is a sequence such that $z_n = x_n$ except for a finite number of indices, the product of general factor $z_n$ is convergent.