1/(2×4)=1/2×(1/2-1/4)
同理,可得
1/(2×4)+1/(4×6)+1/(6×8)+……+1/(2008×2010)
=1/2×(1/2-1/4)+1/2×(1/4-1/6)+……+1/2×(1/2008-1/2010)
=1/2×(1/2-1/4+1/4-1/6+……+1/2008-1/2010)
=1/2×(1/2-1/2010)
=1/2×1004/2010
=502/2010
=251/1005
1/(2×4)=1/2×(1/2-1/4)
同理,可得
1/(2×4)+1/(4×6)+1/(6×8)+……+1/(2008×2010)
=1/2×(1/2-1/4)+1/2×(1/4-1/6)+……+1/2×(1/2008-1/2010)
=1/2×(1/2-1/4+1/4-1/6+……+1/2008-1/2010)
=1/2×(1/2-1/2010)
=1/2×1004/2010
=502/2010
=251/1005