A = 1 . 2 . 3 + 2 . 3 . 4 + ......... + 38 .39 . 40
\(\Rightarrow4A=1.2.3.4+2.3.4.4+......+38.39.40.4\)
\(\Rightarrow4A=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+.......+38.39.40.\left(41-37\right)\)
\(\Rightarrow4A=1.2.3.4+1.2.3.0+2.3.4.5-1.2.3.4+....+38.39.40.41-38.39.40.37\)
\(\Rightarrow4A=38.39.40.41\)
\(\Rightarrow A=\frac{38.39.40.41}{4}\)
\(\Rightarrow A=38.39.10.41\)
\(\Rightarrow A=607620\)
Vậy \(A=607620\)