1*3/1+2*4/1+3*5/1+4*6/1+5*7/1+6*8/1+7*9/1+8*10/1+9*11/1+10*12/1
=(1-1/3 +1/2-1/4 +1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/8-1/10+1/9-1/11+1/10-1/12)/2
=(1+1/2-1/11-1/12)/2
=175/264
1*3/1+2*4/1+3*5/1+4*6/1+5*7/1+6*8/1+7*9/1+8*10/1+9*11/1+10*12/1
=(1-1/3 +1/2-1/4 +1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/8-1/10+1/9-1/11+1/10-1/12)/2
=(1+1/2-1/11-1/12)/2
=175/264