Calculating $\lim\limits_{n\to\infty}\frac{(\ln n)^{2}}{n}$ What is the value of $\lim\limits_{n\to\infty}\dfrac{(\ln n)^{2}}{n}$ and the proof ?
I can't find anything related to it from questions.
Just only $\lim\limits_{n\to\infty}\dfrac{\ln n}{n}=0$, which I know it is proved by Cesàro.

There's for sure an easier way, but if we use L'Hospital we get
\begin{align}
\frac{d}{dn}\Bigl[ \frac{\ln(n)^2}{n} \Bigr] &= -\frac{(\ln(n)-2)\ln(n)}{n^2}
\\ &=- \frac{\ln(n)^2}{n^2} + 2\frac{\ln(n)}{n^2}
\end{align}
And you should be able to continue from this, knowing something about $\frac{\ln(n)}{n}$.
