1/2*4+1/4*6+1/6*8+····+1/2006*2008=几
来源:百度知道 编辑:UC知道 时间:2024/05/29 05:53:18
要详细步骤
1/(2*4)=(1/2-1/4)*1/2
1/(4*6)=(1/4-1/6)*1/2
......
1/(2006*2008)=(1/2006-1/2008)
1/2*4+1/4*6+1/6*8+····+1/2006*2008
=1/2*(1/2-1/4+1/4-1/6+...+1/2006-1/2008)
=1/2*(1/2-1/2008)
=1/2*1003/2008
=1003/4016
使用错项法~~
原式=1/2*(1/2-1/4+1/4-1/6+1/6-1/8....+1/2006-1/2008)=1/2*(1/2-1/2008)=1003/4016
因为分母是差2所以要提取1/2
若是1/3*7+1/7*11....这种就要提取1/4
要举一反三~~~
希望能对您有帮助!!!
1/(2*4)=(1/2-1/4)*1/2
1/(4*6)=(1/4-1/6)*1/2
......
1/(2006*2008)=(1/2006-1/2008)
1/2*4+1/4*6+1/6*8+····+1/2006*2008
=1/2*(1/2-1/4+1/4-1/6+...+1/2006-1/2008)
=1/2*(1/2-1/2008)
=1/2*1003/2008
=1003/4016
1/n*(n+2)=(1/n - 1/n+2)/2 (右边通分一下就可以得到左边)
原式=(1/2)*(1/2-1/4+1/4-1/6+1/6……-1/2006+1/2006-1/2008)
=0.5*(1/2-1/2008)
=1003/4016
(1/2) (1/4+1/6)=
1/2*4+1/4*6+1/6*8+.......+1/2006*2008
1/2*4+1/4*6+1/6*8+1/48*50
1/2+1/4+1/6+1/8+.......+1/n=?
2*4/1+4*6/1+6*8/1+8*10/1+10*12/1
|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+....+|1/2006-1/2004|
|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+.....+|1/2006-1/2004|
|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006|
1/1*3+1/2*4+1/3*5+1/4*6+...+1/9*11
(2/1+3/1+4/1+5/1)乘(2/1+3/1+4/1+5/1+6/1)减(2/1+3/1+4/1+5/1+6/1)乘(2/1+3/1+4/1+5/1)等于多少