Question

tính:1*2+2*3+3*4+...+19*20

Answer 1

Đặt \(A=1.2+2.3+...+19.20\)

\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+...+19.20.\left(21-18\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+...+19.20.21-18.19.20\)

\(\Rightarrow3A=19.20.21\)

\(\Rightarrow A=19.20.7=2660\)

Vậy A = 2660

Answer 2

Đặt A = 1.2 + 2 . 3 + 3 . 4 + ... + 19 . 20

3A = 3(1.2 + 2 . 3 + 3 . 4 + ... + 19 . 20)

= 1.2.3 + 2.3.3 + 3.3.4 + ...+ 3.19.20

= 1.2.3 + 2.3.(4-1) + ... + 19 . 20 . (21- 18)

= 1.2.3 + 2.3.4 + 1.2.3 + ... + 19.20.21 + 18.19.20

= 19 . 20 .21

= 7980