2*4/1+6*8/1+…+2006*2008/1+4*6/1+8*10/1+…2004*2006/1等于几
问题描述：
2*4/1+6*8/1+…+2006*2008/1+4*6/1+8*10/1+…2004*2006/1等于几
答
2*4/1+6*8/1+…+2006*2008/1+4*6/1+8*10/1+…2004*2006/1
=1/2(1/2-1/4)+1/2(1/4-1/6)+…+1/2(1/2006-1/2008)
=1/2(1/2-1/4+1/4-1/6+1/6-…+1/2006-1/2008)=1/2(1/2-1/2008)
=1003/4016
答
1/2*4+1/4/6+1/6*8+……+1/2004*2006+1/2006*2008
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2004-1/2006+1/2006-1/2008)
=1/2*(1/2-1/2008)
=1/2*1003/2008
=1003/4016