六年级数学题1/3*4+1/4*5+1/5*6+...+1/99*100

1/3*4+1/4*5+1/5*6+...+1/99*100
=(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+........+(1/99-1/100)
=1/3-1/4+1/4-1/5+1/5-1/6+........+1/99-1/100
=1/3-1/100
=97/300

an=1/ （n+1）*n
=〔(n+1)-n〕/ (n+1)*n
=(n+1)/(n+1)*n - n/(n+1)*n
=1/n-1/(n+1)
1/3*4=1/3-1/4
1/4*5=1/4-1/5
1/5*6=1/5-1/6
…………
1/99*100=1/99-1/100
所以
原式=（1/3-1/4）+（1/4-1/5）+（1/5+ ………… -1/99）+（1/99-1/100）
=1/3-1/100
=97/300

1/3*4=1/3-1/4
同理
1/4*5=。。。。。。
故原式1/3-1/100=97/300

1/3*4+1/4*5+1/5*6+...+1/99*100
=1/3-1/4+1/4-1/5+1/5-1/6....+1/99-1/100
=1/3-1/100
=97/300

1/n(n+1)=1/n- 1/(n+1)
结果=1/3 -1/100=97/300

1/3*4+1/4*5+1/5*6+...+1/99*100 =(1/3-1/4)+(1/4-1/5)+.....+(1/99-1/100)=1/3-1/100=97/300