SIMON-MARAIS 2023 A4

Let $x_0, x_1, x_2, \ldots$ be a sequence of positive real numbers such that for all $n \geq 0$ ,

$x_{n+1} = \frac{(n^2 + 1)x_n^2}{x_n^3 + n^2}.$

For which values of $x_0$ is this sequence bounded?

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Solutions

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