1/(1×3)+1/(2×4)+1/(3×5)+……+1/(9×11)=?

问题描述:

1/(1×3)+1/(2×4)+1/(3×5)+……+1/(9×11)=?

原式=(1-1/3+1/2-1/4+1/3-1/5+……+1/9-1/11)/2 =(1+1/2-1/10-1/11)/2 =(3/2-21/110)/2 =72/110 =36/55