Does the following infinite product converge to a non-zero value?
$$\prod_{t=1}^{\infty}\left(1-\frac{1}{1.127^t}\right)$$
Mathworld gives a formula (ref 46 & 47) which, given that $1.127 > 1$, seems to imply that this is the case, but I may have misunderstood as I can't claim any knowledge of the Jacobi theta function used in (47).
The series $\sum_{t=1}^\infty(1.127)^{-t}$ converges (the sum of a geometric progression with ratio $<1$), and hence, by the well-known theorem, your infinite product converges. (The definition of convergence of an infinite product includes the condition that the limit is nonzero.)