[ام زيزو]

voici la solution de l'exercice 93 page 174
U1=0 U2=-1/2 U3=-3/4
2-
لدينا Vn=Un+e
و Vn+1=Un+1 +é
Vn+1=Un -1/2 +é
=Un-1 +2é/2
=1/2(Un+é)+(é-1)/2
=1/2 Vn+(é-1)/2
Vn+1/Vn=1
E=1
Vn=Un+é
V0=U0+é
=2
Vn=2.(1/2)n
Vn=Un+1
Un=Vn-1
Un=2.(1/2)n-1
Un+1-Un= 2.(1/2)n+1 -1-2.(1/2)n
=2(1/2)n .1/2 -2.(1/2)n
=2(1/2)n (-1/2
منه Un متناقصة
lUn+1l<10-4
Vn<10-4
2.(1/2)n<10-4
N=15
Sn=5-n-(1/2)n-1
Lim Sn/n =-1