Question

Tính: 1×3+3×5+5×7+•••+15×17+17×19

Answer 1

Đặt A = 1.3 + 3.5 + 5.7  + ... + 15.17 + 17.19 

6A = 1.3.6 + 3.5.6 + .... + 15.17.6 + 17.19.6 

6A = 1.3.(5 + 1) + 3.5.(7 - 1) + ... + 15.17.(19 - 13) + 17.19.(21 - 15)

6A = 1.3.5 + 1.3 + 3.5.7 - 1.3.5 + ... + 15.17.19 - 13.15.17 + 17.19.21 - 15.17.19

6A = (1.3.5 + 3.5.7 + ... + 15.17.19 + 17.19.21) - ( 1.3.5 + ... + 13.15.17 + 15.17.19) + 1.3

6A = 17.19.21 + 1.3

6A = 6783 + 3 

6A = 6786

A = 6780 : 6 = 1131