\(A=1.2+2.3+3.4+...+99.100\)
\(\Rightarrow3A=3.\left(1.2+2.3+3.4+...+99.100\right)\)
\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+99.100.3\)
\(\Rightarrow3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)
\(\Rightarrow3A=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)
\(\Rightarrow3A=99.100.101\)
\(\Rightarrow A=\frac{99.100.101}{3}\)
Ta có: A= \(1.2+2.3+3.4+....+99.100\)
=> \(3A=1.2.3+2.3.3+3.4.3+....+99.100.3\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....+99.100.101-98.99.100\)
\(\Rightarrow3A=99.100.101\)
\(\Rightarrow3A=999900\)
\(\Rightarrow A=333300\)
