1/(12)+1/(123)+1/(1234)+……+1/(123*4……100)99/100

来源：学生作业帮助网编辑：六六作业网时间：2024/12/26 22:31:55

1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)99/1001/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4

1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)99/100
1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)
99/100

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