等差数列共2005项,偶数项与奇数项之比为?

你说的应该是偶数项和与奇数项和之比吧.
若n为奇数,S偶/S奇=(n-1)/(n+1)=1002/1003.
理由如下：S奇=(a1+an)*|n/2|/2=(a1+(a1+nd))*(n+1)/4 = (2a1+nd)*(n+1)/4
S偶=(a2+An-1)*|n/2|/2=((a1+d)+(a1+(n-1)d))*(n-1)/4 = (2a1+nd)*(n-1)/4
总结一下：等差数列｛an｝中,公差为d,则
1、n为奇数：
S奇-S偶=(2a1+nd)/2；S奇/S偶=(n+1)/(n-1),
因为：S奇=(a1+an)*|n/2|/2=(a1+(a1+nd))*(n+1)/4 = (2a1+nd)*(n+1)/4
S偶=(a2+An-1)*|n/2|/2=((a1+d)+(a1+(n-1)d))*(n-1)/4 = (2a1+nd)*(n-1)/4
2、n为偶数：
则 S奇=(a1+An-1)*|n/2|/2=(a1+a1+(n-1)d)*n/4 = (2a1+nd-d)*n/4
S偶=(a2+An)*|n/2|/2=(a1+d+a1+nd)*n/2/2 = (2a1+nd+d)*n/4
所以 S奇-S偶=-2d*n/4=-dn/2；S奇/S偶=(2a1+nd-d)/(2a1+nd+d)

（a1+a3+……+a2005)/(a2+a4+……+a2004）=0.5【a1+a2005]*1003/0.5[a2+a2004]*1002
=1003/1002
等差数列===>a1+a2005=a2+a2004