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> Let $\{x\_n\}$ be a sequence of real numbers such that $0< x\_1 <x\_2$. If $$x\_n= \frac{2}{\frac{1}{x\_{n-1}}+\frac{1}{x\_{n-2}}}, $$then show that 
>  $$\lim\_{n\to\infty}x\_n=\frac{3x\_1x\_2}{2x\_1+x\_2}.$$
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