In the text "Function Theory of a Complex Variable" the definition and conditions for convergence for an Infinite product is given in $(1.)$ i'm initially having trouble discerning whether both conditions have to be met for the convergence of a product.
$(1.)$
An infinite product: $$\prod_{j=1}^{\infty} (1+a_{j})$$
is said to converge if
$(1.)$ only a finite number $a_{j_{i}}, \cdot \cdot \cdot, a_{j_{k}}$ of those $a_{j}$'s are equal to $-1$
$(2.)$ if $N_{o} > 0$ is so large that $a_{j} \neq -1$ for $j > N_{o}$, then:
$$\lim_{N \rightarrow \infty} \prod_{j = N_{o} +1 }(1+a_{j})$$