1/(12)+1/(23)+1(34)+1/（45）……1/（9899）+1/（99+100)=?

来源：学生作业帮助网编辑：六六作业网时间：2024/12/24 00:47:24

1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99+100)=?1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/

1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99+100)=?
1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99+100)=?

1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99+100)=?
1/(1*2)+1/(2*3)+1*(3*4)+1/（4*5）……1/（98*99）+1/（99*100)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/98-1/99+1/99-1/100
=1-1/100
=99/100