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## Homework Statement

Let [itex](a_n)_{n\in\mathbb{N}}[/itex] be a real sequence such that [itex]a_0\in(0,1)[/itex] and [itex]a_{n+1}=a_n-a_n^2[/itex]

Does [itex]\lim_{n\rightarrow\infty}na_n[/itex] exist? If yes, calculate it.

## Homework Equations

## The Attempt at a Solution

I have a solution but I'd like to see other solutions..