1/(1×4)+1/(4×7)+1/(7×10)+1/(10×13)+···+1/(2008×2011)
=(1-1/4)/3+(1/4-1/7)/3+...+(1/2008-1/2011)/3
=(1-1/4+1/4-1/7+...+1/2008-1/2011)/3
=(1-1/2011)/3
=670/2011