解:1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+…+100）=2/(2*3)+2/(3*4)+2/(4*5)+…+2/(100*101)=2*[1/(2*3)+1/(3*4)+1/(4*5)+…+1/(100*101)]=2*(1/2-1/3+1/3-1/4+1/4-1/5+…+1/100-1/101)=2*(1/2-1/101)=99/101.
