化简:1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10

来源:学生作业帮助网 编辑:作业帮 时间:2024/03/29 20:38:39
化简:1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10

化简:1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10
化简:1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10

化简:1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10
=(1-1/2)+(1/2-1/3)+.+(1/9-1/10)
=1-1/2+1/2-1/3+1/3-...-1/9+1/9-1/10
=1-1/10
=9/10

原式=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+1/8-1/9+1/9-1/10
=1-1/10
=9/10
根据1/n*(n+1)=1/n-1/n+1