Xét\(3A=1\cdot2\left(3-0\right)+2\cdot3\left(4-1\right)+\cdot\cdot\cdot+99\cdot100\left(101-98\right)\)
\(3A=1\cdot2\cdot3-0\cdot1\cdot2+2\cdot3\cdot4-1\cdot2\cdot3+...+99\cdot100\cdot101-98\cdot99\cdot100\)
\(3A=99\cdot100\cdot101\)
\(\Rightarrow A=33\cdot100\cdot101=30300\)
A = 1 . 2 + 2 . 3 + 3 . 4 + ... + 99 . 100
3A = 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + ... + 99 . 100 . 3
3A = 1 . 2 . ( 3 - 0 ) + 2 . 3 . ( 4 - 1 ) + 3 . 4 . ( 5 - 2 ) + ... + 99 . 100 . ( 101 - 98 )
3A = 1. 2 . 3 - 0 . 1 . 2 6 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 + 2 . 3 . 4 + ... + 99 . 100 . 101 - 98 . 99 . 100
3A = ( 1 . 2 . 3 - 1 . 2 . 3 ) + ( 2 . 3 . 4 - 2 . 3 . 4 ) + ... + ( 98 . 99 . 100 - 98 . 99 . 100 ) + ( 99 . 100 . 101 - 0.1 . 2 )
3A = 0 + 0 + 0 + ... + 0 + 99 . 100 . 101 - 0 . 1 . 2
3A = 99 . 100 . 101 - 0
A = \(\frac{99\cdot100\cdot101}{3}=333300\)
\(35\cdot34+35\cdot86+65\cdot75+65\cdot45=35\left(34+86\right)+65\left(75+45\right)\)
\(=35\cdot120+65\cdot120\)
\(=120\left(35+65\right)\)
\(=120\cdot100=12000\)
