Tính nhanh:\(\frac{\left(1+2\right)\times3}{\left(2+3\right)\times4}+\frac{\left(2+3\right)\times4}{\left(3+4\right)\times5}+...+\frac{\left(999+1000\right)\times1001}{\left(1000+1001\right)\times1002}+\frac{\left(1000+1001\right)\times1002}{\left(1001+1002\right)\times1003}\)