1/(2*4)+1/(4*6)+1/(6*8)一直加到1/(2006*2008)等于多少?

式子乘以2得
2/(2*4)+2/(4*6)+2/(6*8)+.....+2/(2006*2008)
= （1/2 - 1/4) + (1/4 - 1/6) + .... + (1/2006 - 1/2008)
= 1/2 - 1/2008
= 1004/2008 - 1/2008
= 1003/2008
故原式子为1003/4016

=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+.......+1/2006-1/2008)
=1/2(1/2-1/2008)
=.....剩下的自己算吧~

1/(2×4)+1/4×6+1/(6×8)……+1/(2006×2008)
=(1/2-1/4)/2+(1/4-1/6)/2+91/6-1/8)/2+...+(1/2006-1/2008)/2
=(1/2-1/2008)/2
=1003/2008*1/2
=1003/4016

=1/2(1/2-1/4+1/4-1/6+....+1/2006-1/2008)
=1/2(1/2-1/2008)
=1003/4016