A= 1.2 + 2.3 + 3.4 +...+ 2011.2012
=>3A= 1.2.3 + 2.3.3 + 3.4.3 +...+ 2011.2012.3
3A= 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) +...+ 2011.2012.(2013 - 2010)
3A= (1.2.3 + 2.3.4 + 3.4.5 +...+ 2011.2012.2013) - (0.1.2 + 1.2.3 + 2.3.4 +...+ 2010.2011.2012)
3A= (2011.2012.2013) - (0.1.2)
3A= 8144863716 - 0
\(A=\frac{8144863716}{3}=2714954572\)
Vậy A= 2714954572