1/(1×3)=1/2*(1-1/3),1/(2×4)=1/2*(1/2-1/4),1/(3×5)=1/2*(1/3-1/5),…,1/(9×11)=1/2*(1/9-1/11)
所以原式=1/2*(1-1/3+1/2-1/4+1/3-1/5+……+1/9-1/11)
=1/2*(1-1/11+1/2-1/10)
=1/2*(10/11+2/5)
=1/2*72/55
=36/55
1/(1×3)=1/2*(1-1/3),1/(2×4)=1/2*(1/2-1/4),1/(3×5)=1/2*(1/3-1/5),…,1/(9×11)=1/2*(1/9-1/11)
所以原式=1/2*(1-1/3+1/2-1/4+1/3-1/5+……+1/9-1/11)
=1/2*(1-1/11+1/2-1/10)
=1/2*(10/11+2/5)
=1/2*72/55
=36/55