急~~关于初一数学题

来源：百度知道 编辑：UC知道 时间：2024/06/07 09:20:49
题目:

1/2X4+1/4X6+1/6X8+...+1/2004X2006

是 2X4 分之 1 ..这样

付详细的解题过程~~(步骤) 谢谢

在线等

急~~小弟只有20分全贡献了~~~

1/2X4+1/4X6+1/6X8+...+1/2004X2006
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2004-1/2006)
=1/2*(1/2-1/2006)
=1/4-1/4012
=501/2006

=1/2*(1/2-1/4+1/4-1/6+……+1/2004-1/2006)=501/2006

1/[n(n+2)]=0.5[1/n-1/(n+2)]
所以原式变成了
0.5（1/2-1/4+1/4-1/6……+1/2004-1/2006）
=0.5（1/2-1/2006）
=0.5（1002/2006）
=501/2006

原式=(1/2-1/4+1/4-1/6....1/2004-1/2006)/2=501/2006

1/2X4+1/4X6+1/6X8+...+1/2004X2006
=1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+...-1/2004+1/2004-1/2006
=1/2-1/2006
=1002/2006
=551/1003

1/(2*4)+1/(4*6)+1/(6*8)+…+1/(2004*2006)
=(1/4)[1/(1*2)+1/(2*3)+1/(3*4)+…+1/(1002*1003)]
=(1/4)[(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/1002-1/1003)]
=(1/4)(1-1/1003)
=(1/4)(1002/1003)
=501/2006