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 $\sum_{i=1}^{\infty} x_i < \infty$.

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