exo7 4703

$u_0 = a > 1$, $u_{n+1} = \frac 12\left(u_n + \frac a{u_n}\right)$.

$0 < u_0 < \frac {\sqrt5-1}2$, $u_{n+1} = 1 - u_n^2$.

$u_{n+1} = u_n-u_n^2$.

$u_0 = 0$, $u_{n+1} = u_n^2+\alpha$.

$u_{n+1} = u_n + \frac{1+u_n}{1+2u_n}$.

$u_0 \in\, [0,1]$, $u_{n+1} = \frac{\sqrt{u_n}}{\sqrt{u_n}+\sqrt{1-u_n}}$.

$u_{n+1} = \sqrt{2-u_n}$.

$u_{n+1} = \sqrt{4-3u_n}$.

$u_{n+1} = \frac{u_n-\ln(1+u_n)}{u_n^2}$.

$u_{n+1} = \frac3{2u_n^2+1}$.

$u_0 > 0$, $u_{n+1} = u_n^\alpha$.

$u_0 > 0$, $u_{n+1} = \alpha^{u_n}$.