Let $(a_n{)}_{n\in \mathbb{N}}$ be a sequence of complex numbers. If $\underset{N\to \mathrm{\infty }}{lim}\prod _{n=1}^N(1+a_n)=p$ and $p\ne 0$, then we say that $\prod _{n=1}^{\mathrm{\infty }}(1+a_n)$ 1;;converges to $p$.

If $\underset{N\to \mathrm{\infty }}{lim}\prod _{n=1}^N(1+a_n)=0$ but there are only finitely many terms $a_k=-1$, and the product still converges if we remove these terms, then we say that the sum 1;;converges to 0.

If all $1+a_n\ne 0$, but we still have that $\underset{N\to \mathrm{\infty }}{lim}\prod _{n=1}^N(1+a_n)=0$, then we say that this product 1;;diverges to zero.