因为1/n(n+2)=[1/n-1/(n+2)]/2
所以1/1*3+1/2*4+1/3*5+...+1/9*11
=[(1-1/3)+(1/2-1/4)+(1/3-1/5)+...+(1/9-1/11)]/2
=(1+1/2-1/10-1/11)/2
=36/55
希望能解决您的问题.