1/n(n+1)=1/n-1/(n+1)
1+1/2+1/6+1/12+1/20+……+1/4030056+1/4034072
=1+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+------+1/2007-1/2008+1/2008-1/2009
=2-1/2009
=4017/2009
1+1/2+1/6+1/12+1/20+……+1/4030056+1/4034072
1/n(n+1)=1/n-1/(n+1)
1+1/2+1/6+1/12+1/20+……+1/4030056+1/4034072
=1+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+------+1/2007-1/2008+1/2008-1/2009
=2-1/2009
=4017/2009