Sagot :
a)x0=0
x1=1
x2=1+2*0=1
x3=1+2*1=3
x4=3+2*1=5
x5=5+2*3=11
xn=x(n-1)+2*x(n-2)
xn-x(n-1)-2*(x-2)=0
r^2-r-2=0
∆=1+8=9
r1=(1+3)/2=2
r2=(1-3)/2=-1
xn=a*(2^n)+b(-1)^n
x0=0
0=a+b==> a=-b
x1=1
1=a*2-b=-3b
b=(-1/3)
a=1/3
xn=(1/3)*(2^n)-(1/3)*(-1)^n
b)x0=1
x1=1
x2=2
x3=3
x4=5
x5=8
xn=x(n-1)+x(n-2)
xn-x(n-1)-x(n-2)=0
r^2-r-1=0
∆=1+4=5
r1=(1+√5)/2
r2=(1-√5)/2
xn=a(r1)^n+b(r2)^n
x0=1
a+b=1 ==> b=1-a
x1=1=a(1+√5)/2+b(1-√5)/2
a=(√5+5)/10
b=(5-√5)/5
xn=((√5+5))/10*(1+√5)/2)^n+((5-√5)/5)*(1-√5)/2)^n
