1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+100)=2/(1×2)+2/(2×3)+2/(3×4)+.+2/(100×101)=2[1/(1×2)+1/(2×3)+1/(3×4)+.+1/(100×101)]=2(1-1/2+1/2-1/3+1/3-1/4+.+1/100-1/101)=2(1-1/101)=200/101