Consider the equation $$ \frac{\ln\left(x\right)}{x}=\frac{1}{n} $$
I've shown that on $\left[1,e\right]$, there's a unique solution $a_n$. The sequence $\left(a_n\right)$ decreases and $a_n \geq 1$ so the sequence converges. I know that the limit of $a_n$ is $1$, how can I show it ? Any hint ?
Edit : Am I allowed to right that it implies $Ln(l)/l=0$ ?