1/2×4+1/4×6+1/6×8+…1/2006×2008=?1/2×4这样的是2×4分之1
问题描述：
1/2×4+1/4×6+1/6×8+…1/2006×2008=?
1/2×4这样的是2×4分之1
答
1/4 X [(1 - 1/2) + (1/2 - 1/3) + (1/3 -1/4) ...... + (1/1002 -1/1003) +(1/1003 - 1/1004)]
=1/4 X ( 1 - 1/1004)
=1003/4016
答
1/2×4+1/4×6+1/6×8+…1/2006×2008
=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