51问答网 > 1⼀1*2*3+1⼀2*3*4+1⼀3*4*5+…+1⼀8 *9*10+1⼀9*10*11

1⼀123+1⼀234+1⼀345+…+1⼀8 910+1⼀91011

/是分数线

2025-02-27 10:31:35

推荐回答（2个）

回答1：

原式=(1/2)*(1/1*2-1/2*3)+(1/2)*(1/2*3-1/3*4)+……+(1/2)*(1/9*10-1/10*11)
=(1/2)*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/9*10-1/10*11)
=(1/2)*(1/1*2-1/10*11)
=27/110

回答2：

1/n(n+1)(n+2)
=(1/2)*[1/n(n+1)-1/(n+1)(n+2)]
=(1/2)*[1/n-1/(n+1)+1/(n+1)-1/(n+2)]
=(1/2)*[1/n-1/(n+2)]

1/1*2*3+1/2*3*4+1/3*4*5+…+1/8 *9*10+1/9*10*11
=(1/2)*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/8-1/10+1/9-1/11)
=(1/2)*(1+1/2-1/10-1/11)
=36/55