Bonsoir,
1) voir le fichier xls joint.
2)
a)
[tex] v_{0} =\dfrac{1}{1-2}=-1.\\
v_{n+1}-v_{n}=\dfrac{1}{u_{n+1}-2}-\dfrac{1}{u_{n}-2}\\
=\dfrac{1}{\dfrac{u_{n}-4}{u_{n}-3}-2}-\dfrac{1}{u_{n}-2}\\
=\dfrac{u_{n}-3}{-u_{n}+2}-\dfrac{1}{u_{n}-2}\\
=-\dfrac{u_{n}-3+1}{u_{n}-2}\\
=-1[/tex]
b)
[tex]v_{n}=v_{0}+(-1)*n=-1-n=-n-1\\
[/tex]
c)
[tex]v_{n}=\dfrac{1}{u_{n}-2}=-n-1\\
(u_{n}-2)(-n-1)=1\\
u_{n}=\dfrac{2n+1}{n+1}\\
\lim_{n \to \infty} u_n =2[/tex]
