je n'y arrive pas merci a se qui mederon

1/a-1/(a+1)=(a+1)/(a(a+1))-a/(a(a+1))
                 =1/(a(a+1))

1/(1*2)=1/1-1/2
1/(2/3)=1/2-1/3
...
1/(8*9)=1/8-1/9

S=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(8*9)
=(1/1-1/2)+(1/2-1/3)+...+(1/8-1/9)
=1-1/9
=8/9