Les suites: Les suites adjacentes. (2)

2/
Xn=X , Xn+1=X'
on a pr chaque n de N : n.X+X^3=n (1)
pr n+1 : n.X'+X'+X'^3=n+1 (2)

(2)-(1) : n.(X'-X)+X'+X'^3-X^3=1
(X'-X)(n+X²+X'²+XX')=1-X'
on a X'e[0,1] => 1-X'>=0
=> X'>X psq n+X²+X'²+XX'>=0
4/
Sans réccurence : Ing <=> n-1<n.X<n
(1) : n.X+X^3=n => n.X=n-X^3 donc Ing <=> n-1<n-X^3<n
<=> 0<X^3<1