Question

1/2*4+1/4*6+1/6*8+····+1/2006*2008=几

要详细步骤

Answer 1

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

Answer 2

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！！！

Answer 3

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

Answer 4

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