Exercices 4 à 8
Exercice 4
1. (n+1)/(n2+1)
U0=1
U1=1
U2=3/5
U3=2/5
U4= 5/17
U5=3/13
2. u0=1 et u(n+1)=2u(n)
U0= 1
U1= 2
U2= 4
U3= 8
U4= 16
U5= 32
3. U1=-2 et u(n+1)=2u(n)
U1= -2
U2= -3
U3= -5
U4= -9
U5= -17
4. U(n) = ‘racine’ (n2+1)
U1= 1,4142
U2= 2,2360
U3= 3,1622
U4= 4,1231
U5= 5,0990
U0= 1
5. U(n)= 2^n
U0= 1
U1= 2
U2= 4
U3= 8
U4= 16
U5= 32
Exercice 5: u(n)= -3n+5
U(n+1)= -3n+2
U(n)+1= -3n+6
U(n+2)= -3n-1
U(2n)= -6n+5
U(n2)= -3n2+5
U(2n+1)= -6n+2
Exercice 6: u(n)= 7-3n
Calculs:
U2= -2
U3= 1
Exercice 8
U1= 4
Démonstration
Exercice 7
Calculs
U1= -1
U2= 5
U3= -7
Démonstration
U(n+1) = 7- 3(n+1) = (7-3n)-3
U(n+1) = u(n)-3
U[(n+1)+1] = u(n+2) donc
U(n+2)= 3-2[3-2u(n)]
=> U(n+2) = 4u(n)-3