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[itex]\lim\limits_{n\rightarrow\infty}\sup \left\{\frac{n}{x^n}:x\in\left( 1; \infty\right)\right\}[/itex]

It seems to be 0, but what if [itex]x = 1+\frac{1}{n}[/itex]? In that case [itex]x^n = e[/itex] and the above limit is then [itex]+\infty[/itex], isn't it? I have a feeling I'm somehow wrong, but if I'm not, for what x is the above limit equal to 0 ?

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# Confused by a simple limit

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