Bonsoir,
[tex]On\ note\ u_n\ le\ r\'esultat\ apr\`es \ le\ passage\ n\\
u_0=x\\
u_1=2*x-1\\
u_2=2*u_1-1\\
=2*(2x-1)-1\\
=4x-2-1\\
=2^2*x-3\\
=2^2*x-(2^2-1)\\
u_3=2*u_2-1\\
=2*(2^2*x-(2^2-1))-1\\
=2^3*x-2^3+2-1\\
=2^3*x-(2^3-1)\\
=8x-7
c)\\
u_4=2^4*x-(2^4-1)\\
=16x-15\\
d)\\
u_{98}=2^{98}*x-(2^{98}-1)\\
e)\\
2^{98}*x-(2^{98}-1)=2^{100}+1\\
2^{98}*x=2^{100}+1+2^{98}-1\\
x= \dfrac{2^{98}(4+1)}{2^{98}} \\
x=5\\
[/tex]
