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Valeurs de la suite u0=3,  un+1=2un+n
 On tape :rsolve(u(n+1)=2u(n)+n,u(n),u(0)=3) On obtient :[-1+4*2^(n+1-1)-n] 
- Valeurs de la suite u12=1,   un+1=2un+n
 On tape :rsolve(u(n+1)=2u(n)+n,u(n),u(1)^2=1) On obtient :[[-1-(-3)/2*2^(n+1-1)-n,
 -1-(-1)/2*2^(n+1-1)-n]]
 
- Valeurs de la suite u0=3,  un+1=2un+n3n
 On tape :rsolve(u(n+1)=2u(n)+(n)*3^n,u(n),u(0)=3) On obtient :[-3*3^(n+1-1)+6*2^(n+1-1)+n*3^(n+1-1)] 
- Valeurs de la suite  u0=4, un+1=un−1/un−2
 On tape :rsolve(u(n+1)=(u(n)-1)/(u(n)-2),u(n),u(0)=4) On obtient :[((10*sqrt(5)+30)*((sqrt(5)-3)/2)^n+30*sqrt(5)-70)/ (20*((sqrt(5)-3)/2)^n+10*sqrt(5)-30)]
 
- Valeurs de la suite u0=0,u1=1,  un+1=un+un−1 pour n>0.
 On tape :rsolve(u(n+1)=u(n)+u(n-1),u(n),u(0)=0,u(1)=1) On obtient :[(5+sqrt(5))/10*((sqrt(5)+1)/2)^(n+1-1-1)+
 (5-sqrt(5))/10*((-sqrt(5)+1)/2)^(n+1-1-1)]
 
- Valeurs de la suite u0=0,u1=1,  un+1=2*un+un−1+n pour n>0.
 On tape :rsolve(u(n+1)=2*u(n)+u(n-1)+n,u(n),u(0)=0,u(1)=1) On obtient :[(-1)/2-(-2-3*sqrt(2))/8*(sqrt(2)+1)^(n+1-1)-
 (-2+3*sqrt(2))/8*(-sqrt(2)+1)^(n+1-1)-1/2*n]
 Ou on tape :
 rsolve([u(n+1)=2*u(n)+v(n)+n,v(n+1)=u(n)],
 [u(n),v(n)],u(0)=0,v(0)=1) 
On obtient :[[(-1)/2-(-2-3*sqrt(2))/8*(sqrt(2)+1)^(n+1-1)-
 (-2+3*sqrt(2))/8*(-sqrt(2)+1)^(n+1-1)-1/2*n,
 -(-4+sqrt(2))/8*(sqrt(2)+1)^(n+1-1)-
 (-4-sqrt(2))/8*(-sqrt(2)+1)^(n+1-1)-1/2*n]]
 
- Valeurs de la suite u0=0,v0=1,  un+1=un+vn, vn+1=un−vn,.
 On tape :
 rsolve([u(n+1)=u(n)+v(n),v(n+1)=u(n)-v(n)],
 [u(n),v(n)],[u(0)=0,v(0)=1])
 On obtient :[[1/2*2^((n-1)/2)+1/2*(-(sqrt(2)))^(n-1),
 (-1+sqrt(2))/2*2^((n-1)/2)+
 (-1-sqrt(2))/2*(-(sqrt(2)))^(n-1)]]
 
- Valeurs de la suite u0=2,v0=0,  un+1=4*vn+n+1, vn+1=un,.
 On tape :
 rsolve([u(n+1)=4*v(n)+n+1,v(n+1)=u(n)],
 [u(n),v(n)],[u(0)=2,v(0)=0])
 On obtient :[[(-8)/9+2*2^(n+1-1)-(-8)/9*(-1)^(n+1-1)*2^(n+1-1)-
 1/3*n,(-5)/9+2^(n+1-1)-4/9*(-1)^(n+1-1)*2^(n+1-1)-
 1/3*n]]