Suppose we have a sequence $(x_k)_{k \in \mathbb{N}}$ with $-e^{-1} \leq x_k \leq 0 \quad \forall k \in \mathbb{N}$ and $x_k \to 0$ as $k \to \infty$. Is the series $$ \sum_{k=1}^{\infty} W_0 (x_k) $$ necessarily finite? If not, what conditions would we need on $x_k$?
2026-03-31 20:11:59.1774987919
Infinite series involving Lambert W function
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