1-1/2-1/6-1/12-1/20-…-1/（99*100） =1-(1/2+1/6+1/12+1/20+.+1/99*100) =1-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/99-1/100) =1-(1-1/100) =1-99/100 =1/100
麻烦采纳,谢谢!