1*3分之1+2*4分之1+3*5分之1+…+9*11分之1
=1/2(1-1/3)+1/2(1/2-1/4)+1/2(1/3-1/5)+.+1/2(1/9-1/11)
=1/2[1-1/3+1/2-1/4+1/3-1/5+.+1/9-1/11)
=1/2(1+1/2-1/10-1/11)
=1/2(3/2-1/10-1/11)
=1/2(7/5-1/11)
=1/2×72/55
=36/55