51问答网 > 1⼀1*2*3+1⼀2*3*4+1⼀3*4*5+1⼀4*5*6+1⼀5*6*7+1⼀6*7*8+1⼀7*8*9+1⼀8*9*10+1⼀9*10*11计算方法

1⼀123+1⼀234+1⼀345+1⼀456+1⼀567+1⼀678+1⼀789+1⼀8910+1⼀91011计算方法

同上

2024-11-25 14:42:30

推荐回答（1个）

回答1：

1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+1/5*6*7+1/6*7*8+1/7*8*9+1/8*9*10+1/9*10*11
=(1/2)[(1/1*2)-(1/2*3)]+(1/2)[(1/2*3)-(1/3*4)]+(1/2)[(1/3*4)-(1/4*5)]+...+(1/2)[(1/9*10)-(1/10*11)]
=(1/2)[(1/1*2)-(1/2*3)+(1/2*3)-(1/3*4)+(1/3*4)-(1/4*5)+...+(1/9*10)-(1/10*11)]
=(1/2)[(1/1*2)-(1/10*11)]
=(1/2)(1-1/2-1/10+1/11)
=(1/2)(2/5+1/11)
=(1/2)(27/55)
=27/110.