1/1*4+1/4*7+1/7*10+...+1/2005*2008+1/2008*2011
=1/3（1-1/4)+1/3（1/4-1/7)+1/3(1/7-1/10)+.+1/3(1/2005-1/2008)+1/3(1/2008-1/2011)
=1/3（1-1/4+1/4-1/7+1/7-1/10+.+1/2005-1/2008+1/2008-1/2011)
=1/3(1-1/2011)
=1/3(2010/2011)
=670/2011
1/1X4=1/3(1-1/4) 1/4X7=1/3(1/4-1/7) 1/7x10=1/3(1/7-1/10) 1/N(N+3)=1/3(1/N-1/N+3)