Bonjour,
90)
[tex] u_0=0\\u_{n+1}=\sqrt{u_{n}^2+1} [/tex]
[tex] ({u_0})^2=0[/tex]
[tex] ({u_1})^2=({\sqrt{u_{0}^2+1}})^2=u_{0}^2+1=1[/tex]
[tex] ({u_2})^2=({\sqrt{u_{0}^2+1+1}}=^2=u_{0}^2+2=2[/tex]
[tex] ({u_2})^3=({\sqrt{u_{0}^2+2+1}})^2=u_{0}^2+3=3[/tex]
...
[tex] ({u_{n+1}})^2=({\sqrt{u_{n}^2+n+1}})^2=(u_{0})^2+n+1=n+1[/tex]
