1/(1×2)=1/1-1/2
1/(2×3)=1/2-1/3
1/(3×4)=1/3-1/4
所以倒数和为:
1/1-1/2+1/2-1/3+1/3-1/4+……+1/99-1/100
=1-1/100
=99/100