Find
\[
\sup \left[ \sum_{n=1}^{\infty} \frac{1}{\sqrt{n}} \left( \sum_{i=n}^{\infty} x_i^2 \right)^{1/2} \Big/ \sum_{i=1}^{\infty} x_i \right],
\]
where the supremum is taken over all monotone decreasing sequences of positive numbers \( (x_i) \) such that \( \sum_{i=1}^{\infty} x_i < \infty \).