1/1*2*3+1/2*3*4+1/3*4*5+···+1/11*12*13 =1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+1/2*(1/3*4-1/4*5)+...+1/2*(1/11*12-1/12*13)=1/2*(1/1*2-1/12*13)=1/2*77/156=77/312