Find asymptotic of recurrence sequence – math.stackexchange.com
Given a sequence $x_1=\frac{1}{2}$, $x_{n+1}=x_n-x_n^2$. It's easy to see
that it limits to $0$. The question is: is there exists an $\alpha$ such,
that $\lim\limits_{n\to\infty}n^\alpha x_n\neq0$. …
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