Question

Tính nhanh 1×2+2×3+3×4+...+50×51

Answer 1

Đặt A = 1.2 + 2.3 + 3.4 + ... + 50.51

  => 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 50.51.3

             = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + .... + 50.51.(52 - 49)

             = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 50.51.52 - 49.50.51

             = 50.51.52

             = 132600

Vì 3A = 132600

 => A = 44300

Vậy 1.2 + 2.3 + 3.4 + ... + 50.51 = 44300