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What is the right way to solve a problem like this?

Let $x_n$ a sequence of real numbers such that: $$ \lim_{n \to \infty}(x_n - x_{n+2})=0,$$ So try that: $$ \lim_{n \to \infty}\frac{x_n - x_{n+1}}{n}=0.$$

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    It is perhaps interesting that the denominator $n$, which at first sight looks unnecessarily large, cannot be replaced by something substantially smaller, like $\frac{n}{\log n}$.2012-01-03

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