1/(1*2)+1/(2*3)+1/(3*4)+...1/(n*(n-1))=
[1-1/2]+[1/2-1/3]+[1/3-1/4]+...+[1/(n-1)-1/n]=
1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n=1-(1/n)

lim [ 1/(1*2)+1/(2*3)+1/(3*4)+...1/(n*(n-1))]=lim[1-(1/n)]=1