1/2×1/4+1/4×1/6+1/6×1/8+1/8×1/10+.+1/2008×1/2010
=1/2×(1/2-1/4)+1/2×(1/4-1/6)+1/2×(1/6-1/8)+1/2×(1/8-1/10)+……+1/2×(1/2008-1/2010)
=1/2×(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+……+1/2008-1/2010)
=1/2×(1/2-1/2010)
=251/1005
1/2×1/4+1/4×1/6+1/6×1/8+1/8×1/10+.+1/2008×1/2010
=1/2×(1/2-1/4)+1/2×(1/4-1/6)+1/2×(1/6-1/8)+1/2×(1/8-1/10)+……+1/2×(1/2008-1/2010)
=1/2×(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+……+1/2008-1/2010)
=1/2×(1/2-1/2010)
=251/1005