Question

[Em_là_ai]

tính nhanh

B=1x2+2x3+3x4+.....+18x19

Answer 1

[Girl]

\(B=1.2+2.3+3.4+...+18.19\)

\(3B=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+18.19.\left(20-17\right)\)

\(3B=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+18.19.20-17.18.19\)

\(3B=18.19.20\Rightarrow B=\frac{18.19.20}{3}=2280\)

Answer 2

[Xyz OLM]

Ta có :   B = 1 x 2 + 2 x 3 + 3 x 4 +.... + 18 x 19

=> 3B = 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 + ... + 18 x 19 x 3

     3B = 1 x 2 x 3 + 2 x 3 x (4 - 1) + 3 x 4 x (5 - 2) + .... + 18 x 19 x (20 - 17)

     3B = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x3 + 3 x 4 x5 - 2 x 3 x 4 + ... + 18 x 19 x 20 - 17 x 18 x 19

     3B = 18 x 19 x 20

       B = 18 x 19 x 20 : 3 

          = 2280

Vậy B = 2280