[tex] Bonjour;\\\\\\1)\ u_1=\dfrac{50}{15}=\dfrac{10}{3}\ ; \ u_2=\dfrac{\dfrac{100}{3}}{\dfrac{40}{3}}=\dfrac{100}{40}=\dfrac{10}{4}=\dfrac{5}{2}\ ;\ u_3=\dfrac{\dfrac{100}{4}}{\dfrac{50}{4}}=\dfrac{100}{50}=\dfrac{10}{5}=2\ ; [/tex]
[tex] 2)\ r=v_{n+1}-v_n=\dfrac{5}{u_{n+1}}-\dfrac{5}{u_n}=\dfrac{5(10+u_n)}{10u_n}-\dfrac{5}{u_n}\\\\\\=\dfrac{5}{u_n}+\dfrac{1}{2}-\dfrac{5}{u_n}=\dfrac{1}{2}\ .\\\\\\v_0=1\ . [/tex]
[tex] 3)v_n=v_0+nr=1+\dfrac{1}{2}n=\dfrac{2+n}{2}\ .\\\\\\4)\ v_n=\dfrac{5}{u_n}\ ,\ donc\ u_n=\dfrac{5}{v_n} = \dfrac{10}{2+n}\ . [/tex]
