1/2*3+1/3*4+1*4*5.....1/99*100

显示全部楼层 · 2008-3-29 18:52:16

1/2*3+1/3*4+1*4*5.....1/99*100=(1/2)-(1/3)+(1/3)-(1/4)+...+(1/99)-(1/100)=(1/2)-(1/100)=(50-1)/100=49/100.

千问 · 2008-3-29 18:52:16

1/2*3+1/3*4+1*4*5.....1/99*100=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/98-1/99)+(1/99-1/100)=1/2-1/3+1/3-1/4+1/4+...-1/99+1/99-1/100=1/2-1/100=49/100

千问 · 2008-3-29 18:52:16

1/2*3 = 1/2 - 1/31/3*4 = 1/3 - 1/4以此类推原式=1/2 - 1/3 + 1/3 -1/4 +1/4 - ... +1/98 -1/99 + 1/99 -1/100
=1/2 - 1/100
=49/100谢谢