What is the value of(adsbygoogle = window.adsbygoogle || []).push({});

[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 ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Confused by a simple limit

**Physics Forums | Science Articles, Homework Help, Discussion**