Question

找规律题：(1/(1*3))+(1/(2*4))+(1/(3*5)+...+(1/(9*11))的计算过程

Answer 1

1/1*3+1/2*4+1/3*5+1/4*6+……+1/9*11

=(2/1*3+2/2*4+2/3*5+2/4*6+……+2/9*11)/2

=[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+……+(1/8-1/10)+(1/9-1/11)]/2

=(1+1/2-1/10-1/11)/2

=36/55