题目

（1x3）分之1 + （3x5）分之1+ （5x7）分之1 + （7x9）分之1 +（9x11）分之1

提问时间：2021-02-01

答案

1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+(1/9-1/11)/2.
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)/2
=(1-1/11)/2
=(10/11)/2
=5/11