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*3+1/3*4+1/4*5+...+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)=1-1+1/100=1/100
