A=1.2+2.3+3.4+...+99.100
3A=3.(1.2+2.3+3.4+...+99.100)
3A=3.1.2+3.2.3+3.3.4+....+3.99.100
3A=1.2.3+(4-1) .2.3+(5-2).3.4+...+(101-98).99.100
3A=1.2.3+2.3.4- 1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100
3A=99.100.101
A=\(\dfrac{99.100.101}{3}\)
Ta có :
\(A=1.2+2.3+.............+99.100\)
\(\Leftrightarrow3A=1.2.3+2.3.3+...........+99.100.3\)
\(\Leftrightarrow3A=1.2.3+2.3.\left(4-1\right)+......+99.100.\left(101-98\right)\)
\(\Leftrightarrow3A=1.2.3+2.3.4-1.2.3+.....+99.100.101-98.99.100\)
\(\Leftrightarrow3A=99.100.101\)
\(\Leftrightarrow A=\dfrac{99.100.101}{3}=333300\)
