1/2+5/6+11/12+19/20+29/30=简便计算

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 13:09:37
1/2+5/6+11/12+19/20+29/30=简便计算1/2+5/6+11/12+19/20+29/30=简便计算1/2+5/6+11/12+19/20+29/30=简便计算1/2+5/6+11

1/2+5/6+11/12+19/20+29/30=简便计算
1/2+5/6+11/12+19/20+29/30=
简便计算

1/2+5/6+11/12+19/20+29/30=简便计算
1/2+5/6+11/12+19/20+29/30
=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)
=[1-(1-1/2)]+[1-(1/2-1/3)]+[1-(1/3-1/4)]+[1-(1/4-1/5)]+[1-(1/5-1/6)]
=1-1+1/2+1-1/2+1/3+1-1/3+1/4+1-1/4+1/5+1-1/5+1/6
=4+1/6
=4又1/6

4又1/6

1/2+5/6+11/12+19/20+29/30
=1/2+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)
=1/2+1-1/2+1/3+1-1/3+1/4+1-1/4+1/5+1-1/5+1/6
=1+1+1+1+1/6
=25/6

=(1-1/2)+(-1/6)+(1-1/12)+(1-1/20)+(1-1/30)
=1+1+1+1+1-(1/2+1/6+1/12+1/20+1/30)
=5-(30/60+10/60+5/60+3/60+2/60)
=5-5/6
=4又1/6

高手风范不同凡响!
拆项:1/n(n+1)=1/n-1/(n+1)
1/2+5/6+11/12+19/20+29/30
=5-(1/1*2+1/2*3+1/3*4+1/4*5+1/5*6)
=5-(1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)
=5-(1/1-1/6)
=4又1/6