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+1/2-1/2+1/3-1/3+1/4-1/4+1/5-……-1/99+1/100
前面可以互相抵消
=1/100