Sequential limit.

Calculus Level 4

Let \(\{a_n\}\) be a sequence such that \(a_1\in (0,1)\), and for any \(n\geq 1\) : \[a_{n+1}= a_n(1-a_n).\]

Find the value of

\[\lim_{n\to +\infty} \frac{n(1-na_n)}{\ln n}.\]

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