1-1/2-1/6-1/12-1/20-……-1/9900
=1-(1×1/2)-（1/2×1/3）-（1/3×1/4）-(1/4×1/5)-.(1/99×1/100)
=1-(1-1/2)-（1/2-1/3）-（1/3-1/4）-(1/4-1/5)-.(1/99×1/100)
=1-1+1/2-1/2+1/3-1/3+1/4-1/4+1/5-.-1/99+1/100
=1/100