Question

[Phạm Thành Lương]

Tính A = 1X2 + 2X3 + 3X4 +...+19X20

Answer 1

[Hà Minh Trang]

M=1x2+2x3+3x4+xxx+19x20

3M=1x2x3+2x3x3+3x4x3+xxx+19x20x3

3M=1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+xxx+19x20x(21-18)

3M=(1x2x3-0x1x2)+(2x3x4-1x2x3)+(3x4x5-2x3x4)+xxx+(19x20x21-18x19x20)

3M=19x20x21-0x1x2

3M=7980-0

3M=7980

M=7980:3

M=2660

Vậy M=2660

Chúc bạn học tốt nha!!!!! ^^

Answer 2

[Nguyễn Lê Phước Thịnh]

\(A=1\cdot2+2\cdot3+...+19\cdot20\)

\(=1\left(1+1\right)+2\left(2+1\right)+...+19\left(19+1\right)\)

\(=\left(1^2+2^2+...+19^2\right)+\left(1+2+...+19\right)\)

\(=\dfrac{19\left(19+1\right)\left(2\cdot19+1\right)}{6}+\dfrac{19\cdot20}{2}\)

\(=2470+190=2660\)