1/(1+2)+1/(1+2+3)+.+1/(1+2+3+.+100) =2/(2*3)+2/(3*4)+.+2/(100*101) =2(1/2-1/3+1/3-1/4+.+1/99-1/100+1/100-1/101) =2(1/2-1/101) =1-2/101 =99/101
