1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7怎样简便运算?、

Question

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7 怎样简便运算?、

Answer 1

1/1x2+1/3x2+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1-1/8 (上式前括后一项与后括号前一项抵消)
=7/8