2乘5分之1+5乘8分之1+8乘11分之1+……+2006乘2009分之1+2009乘2012分之1 =1/3(1/2-1/5)+1/3(1/5-1/8)+1/3(1/8-1/11)+...+1/3(1/2006-1/2009)+1/3(1/2009-1/2012) =1/3(1/2-1/2012) =1/3x1005/2012 =335/2012
