If $x_1\in(0,1)$ and $x_{n+1}=x_n(1-x_n)$, find $\lim_{n\rightarrow\infty}nx_n$ (Hint: using Stolz–Cesàro theorem)I can prove that $x_n$ monotonically decrease and $\lim_{n\rightarrow\infty}x_n=0$.Professor told me to use Stolz–Cesàro theorem, however I still cannot find the limit $\lim_{n\rightarrow\infty}nx_n$.
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