1/2x3+1/3x4+1/4x5+1/5x6+1/6x7简便计算,做得好的有悬赏

题目

1/2x3+1/3x4+1/4x5+1/5x6+1/6x7简便计算,做得好的有悬赏

答案

1/3x2+1/3x4+1/4x5+1/5x6+1/6x7
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1/2-1/7 (上式前括后一项与后括号前一项抵消)
=5/14