Question

【我一道数学题不会做！大家帮帮忙！】

问题是： 1/2*4+1/4*6+1/6*8+······+1/2004*2006请写出祥细过程！

Answer 1

用裂项思想。

但拿出每个式子看 发现是 1/两个连续偶数 1/2n*2(n+1)
裂开→ 1/2*[1/2n-1/2(n+1)]= 1/n - 1/n+1
这个是通式

然后让n等于1，2，3.... 再相加

即

1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ………… + 1/n - 1/n+1
=1 - 1/n+1
你给到 2004=2*1002 所以 n=1002
所以

原式= 1 - 1/1002+1 = 1002/1003

Answer 2

1/2*4=(1/2-1/4)*1/2
1/4*6=(1/4-1/6)*1/2
1/6*8=(1/6-1/8)*1/2
…………
原式=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+……1/2004-1/2006)
=1/2*(1/2-1/2006)
=(1/2)*(1002/2006)
=501/2006

Answer 3

1/2*4+1/4*6+1/6*8+······+1/2004*2006=1/2(1/2-1/4+1/4-1/6+1/6-1/8...+1/2004-1/2006)
=1/2(1/2-1/2006)
=1/2(1003/2006-1/2006)
=1/2*1002/2006
=501/2006

Answer 4

1/2(1/2-1/4+1/4-1/6+1/6-1/8...+1/2004-1/2006)
=1/2(1/2-1/2006)
=1/2(1003/2006-1/2006)
=1/2*1002/2006
=1001/2006

Answer 5

=1/2*(1/2-1/4)+1/2*(1/4-1/6)+……+1/2*(1/2004-1/2006)
=1/2*(1/2-1/4+1/4-1/6+……+1/2004-1/2006)
中间正负抵消
=1/2*(1/2-1/2006)
=501/2006