1/(12)+1/(23)+1/(34)+L+1/(100101)=

来源：学生作业帮助网编辑：六六作业网时间：2024/11/22 03:17:42

1/(1*2)+1/(2*3)+1/(3*4)+L+1/(100*101)=1/(1*2)+1/(2*3)+1/(3*4)+L+1/(100*101)=1/(1*2)+1/(2*3)+1/(3*4)+

1/(1*2)+1/(2*3)+1/(3*4)+L+1/(100*101)=
1/(1*2)+1/(2*3)+1/(3*4)+L+1/(100*101)=

1/(1*2)+1/(2*3)+1/(3*4)+L+1/(100*101)=
解
1/(1*2)+1/(2*3)+……+1/(100*101)
=(1-1/2)+(1/2-1/3)+……+(1/100-1/101)
=1-1/2+1/2-1/3+1/3-……-1/100+1/100-1/101
=1-1/101
=100/101

有规律：1/n-1/(n+1)=1/[n*(n+1）]
原式=1-1/101=100/101

解
1/(1*2)+1/(2*3)+……+1/(100*101)
=(1-1/2)+(1/2-1/3)+……+(1/100-1/101)
=1+(1/2-1/2)+(1/3-1/3)+……+(1/100-1/100)-1/101
=1-1/101
=100/101
附上
1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
………………
1/n(n+1)=1/n-1/(n+1)