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