ThmDex – An index of mathematical definitions, results, and conjectures.
F12366
Formulation 2
Let $x_0, x_1, x_2, \ldots \in (0, 1]$ each be a D993: Real number.
Then \begin{equation} \lim_{N \to \infty} \prod_{n = 0}^N x_n = 0 \quad \iff \quad \lim_{N \to \infty} \sum_{n = 0}^N (1 - x_n) = \infty \end{equation}