找规律并计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/01 19:07:25

找规律并计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100
找规律并计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100

找规律并计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100
1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+···+(1/100+2/100+···+99/100)
=1/2+1+3/2+2+5/2+……+99/2
=1/2(1+2+3+4+5+……99)
=2475

0=1/2-1/2;
1/2=2/2-1/2;
1/3+2/3=3/2-1/2;
1/4+2/4+3/4=4/2-1/2……
所以:原式=(1+2+3+……+100)/2-101*1/2
=(5050-101)/2
=4949/2.