1+1/2+2/2+1/2+1/3+2/3+3/3+2/3+1/3+……+1/100+2/100+……+100/100+99/100+……+1/100=?计算过程及规律

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/18 05:15:01

1+1/2+2/2+1/2+1/3+2/3+3/3+2/3+1/3+……+1/100+2/100+……+100/100+99/100+……+1/100=?计算过程及规律
1+1/2+2/2+1/2+1/3+2/3+3/3+2/3+1/3+……+1/100+2/100+……+100/100+99/100+……+1/100=?计算过程及规律

1+1/2+2/2+1/2+1/3+2/3+3/3+2/3+1/3+……+1/100+2/100+……+100/100+99/100+……+1/100=?计算过程及规律
=2*(1+1/2+2/2+1/3+2/3+3/3+...+1/100+2/100+...+100/100)-(1+2/2+3/3+...+100/100)
=2*(1+3/2+6/3+10/4+15/5+...101/2)-100
= (2+3+..+101)-100 =5050