Question

1*2*3+1*3*4+1*4*5+1*5*6+1*6*7

Answer 1

Đặt A = 1.2.3 + 1.3.4 + 1.4.5 + 1.5.6 + 1.6.7

=> A = 2.3 + 3.4 +  4.5 + 5.6 + 6.7

=> 3A = 2.3.3 + 3.4.3 + 4.5.3 + 5.6.3 + 6.7.3

=> 3A = 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + 4.5.( 6 - 3 ) + 5.6.( 7 - 4 ) + 6.7.( 8 - 5 )

=> 3A = 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + 4.5.6 - 3.4.5 + 5.6.7 - 4.5.6 + 6.7.8 - 5.6.7

=> 3A = - 1.2.3 + ( 2.3.4 - 2.3.4 ) + ( 3.4.5 - 3.4.5 ) + ( 4.5.6 - 4.5.6 ) + ( 5.6.7 - 5.6.7 ) + 6.7.8

=> 3A = - 1.2.3 + 6.7.8

=> 3A = - 6 . 336

=> 3A = - 2016

=> A = - 2016 : 3

=> A = - 672