1/2+1/6+1/12+1/20+1/30+……+1/4038090
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+.+(1/2009-1/2010)
=1-1/2010
=2009/2010
1/2+1/6+1/12+1/20+1/30+……+1/4038090=?
1/2+1/6+1/12+1/20+1/30+……+1/4038090
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+.+(1/2009-1/2010)
=1-1/2010
=2009/2010