Question

1.2+2.3+3.4+...19.20

Answer 1

Đặt \(A=1.2+2.3+3.4+...+19.20\)

Ta có: \(A=1.2+2.3+3.4+...+19.20\)

        \(3A=1.2.3+2.3.3+3.4.3+...+19.20.3\)

        \(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-1\right)+...+19.20.\left(21-1\right)\)

        \(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+19.20.21-18.19.20\)

        \(3A=19.20.21\)

           \(A=19.20.7\)

           \(A=2660\)

Answer 2

\(1\cdot2+2\cdot3+...+19\cdot20=\frac{1\cdot2\cdot\left(3-0\right)+2\cdot3\cdot\left(4-1\right)+...+19\cdot20\cdot\left(21-17\right)}{3}\)

   \(=\frac{1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+19\cdot20\cdot21-18\cdot19\cdot20}{3}\)\(=\frac{19\cdot20\cdot21}{3}=2660\)

Answer 3

của bạn Tạ Đức Hoàng Anh là đúng đấy