1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)99/100
来源:学生作业学帮网 编辑:学帮网 时间:2024/06/16 01:58:57
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