1/(1×2)+1/(2×3)+1/(3×4)+.+1/(100×101)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/100-1/101)
=1-1/2+1/2-1/3+1/3-1/4+……+1/100-1/101
=1-1/101
=100/1011/[n(n+1)]=1/n-1/(n+1)