1+1/3+1/6+1/10+..+1/2009*1004=

最佳答案 - 由投票者2008-02-29 09:02:01选出

1+1/3+1/6+1/10+..+1/2009*1004
=1+2/6+2/12+2/20+……+2/2009*2008
=1+2*[(1/2)-(1/3)]+2*[(1/3)-(1/4)]+2*[(1/4)-(1/5)]+……+2*[(1/2008)-(1/2009)]
=1+2*[(1/2)-(1/2009)]
=2-2/2009
=4016/2009