作业帮1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)99/100
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/16 12:44:47
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