Ta có:
\(A=1.2.3+2.3.4+3.4.5+...+98.99.100\)
\(\Rightarrow4A=1.2.3.4+2.3.4.4+3.4.5.4+...+98.99.100.4\)
\(\Rightarrow4A=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+...+98.99.100.\left(101-97\right)\)
\(\Rightarrow4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...98.99.100.101-97.98.99.100\)
\(\Rightarrow4A=98.99.100.101\)
\(\Rightarrow A=\dfrac{98.99.100.101}{4}\)
Vậy \(A=\dfrac{98.99.100.101}{4}\)
Ta có: \(A=1.2.3+2.3.4+3.4.5+...+98.99.100\)
\(4A=\left(1.2.3+2.3.4+...+98.99.100\right)4\)
\(4A=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)...+98.99.100.\left(101-97\right)\)
\(4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+98.99.100.101-97.98.99.100\)
\(4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+...+97.98.99.100-97.98.99.100+98.99.100.101\)
\(4A=98.99.100.101\)
\(\Rightarrow A=\dfrac{98.99.100.101}{4}=24497550\)