How Do I Find \(x_n\) First?

Calculus Level 4

Let \(\{x_n\}\) be a sequence such that \(x_1=1,\ x_nx_{n+1}=2n\) for \(n\ge 1\).

Find \(\displaystyle \lim_{n\to\infty} \dfrac{|x_{n+1}-x_n|}{\sqrt{n}}.\)

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