# 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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