这四道题用简便方法1/1*2+1/2*3+1/3*4+1/4*5= 1/1*6+1/6*11+1/11*16+1/16*21= 1/6+1/12+1/20+1/30+1/42+1/56= 1/8+1/24+1/48+1/120=

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/12 06:02:32
这四道题用简便方法1/1*2+1/2*3+1/3*4+1/4*5= 1/1*6+1/6*11+1/11*16+1/16*21= 1/6+1/12+1/20+1/30+1/42+1/56= 1/8+1/24+1/48+1/120=

这四道题用简便方法1/1*2+1/2*3+1/3*4+1/4*5= 1/1*6+1/6*11+1/11*16+1/16*21= 1/6+1/12+1/20+1/30+1/42+1/56= 1/8+1/24+1/48+1/120=
这四道题用简便方法
1/1*2+1/2*3+1/3*4+1/4*5=
1/1*6+1/6*11+1/11*16+1/16*21=
1/6+1/12+1/20+1/30+1/42+1/56=
1/8+1/24+1/48+1/120=

这四道题用简便方法1/1*2+1/2*3+1/3*4+1/4*5= 1/1*6+1/6*11+1/11*16+1/16*21= 1/6+1/12+1/20+1/30+1/42+1/56= 1/8+1/24+1/48+1/120=
一、1/1*2+1/2*3+1/3*4+1/4*5=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)=1-1/5=4/5
二、1/1*6+1/6*11+1/11*16+1/16*21=(1-1/6+1/6-1/11+1/11-1/16+1/16-1/21)/5=(1-1/21)/5=4/21
三、1/6+1/12+1/20+1/30+1/42+1/56=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)=1/2-1/8=3/8
四、这题是不是少写了一个啊,应该是1/8+1/24+1/48+1/80+1/120吧
1/8+1/24+1/48+1/80+1/120=(1/2+1/6+1/12+1/20+1/30)/4=(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)/4=(1-1/6)/4=5/24