1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100)=2/(2x3)+2/(3x4)+……+2/(100x101)=2x(1/2-1/3+1/3-1/4+……+1/100-1/101)=2x(1/2-1/101=1-2/101=99/101
