Question

Tính nhanh

1.2 3+2.3.4+3.4.5+4.5.6+.....+20.21.22

 

 

Answer 1

B=1.2.3+2.3.4+4.5.6+....+20.21.22

=>4B=4(1.2.3+2.3.4+3.4.5+...+20.21.22)

=>4B=1.2.3.4+2.3.4.4+3.4.5.4+...+20.21.22.4

=>4B=1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+...+20.21.22(23-19)

=>4B=1.2.3.4+2.3.4.5-2.3.4+3.4.5.6-2.3.4.5+...+20.21.22.23-19.20.21.22

=>4B=20.21.22.23

=>4B=212520

=>B=53130

mình nha

Answer 2

Đặt A = 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 + 4 . 5 . 6 + ... + 20 . 21 . 22

=> 4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . 4 + 3 . 4 . 5 . 4+ 4 . 5 . 6 . 4 + ... + 20 . 21 . 22 . 4

=> 4A = 1 . 2 . 3 . ( 4 - 0 ) + 2 . 3 . 4 . ( 5 - 1 ) + 3 . 4 . 5 . ( 6 - 2 ) + 4 . 5 . 6 . ( 7 - 3 ) + ... + 20 . 21 . 22 . ( 23 - 19 )

=> 4A = 1 . 2 . 3 . 4 - 0 + 2 . 3 . 4 . 5 - 1 . 2 . 3 . 4 + 3 .4 . 5 . 6 - 2 . 3 . 4 . 5 + 4 . 5 . 6 . 7 - 3 . 4 . 5 . 6 + ... + 20 . 21.22.23 - 19.20.21.22

=> 4A = 0 + 20 . 21 . 22 . 23 

=> 4A = 212520

=> A = \(\frac{212520}{4}=53130\)