Question

1 .2 . 3 + 2 . 3 .4 + 3 . 4. 5 +....... + 48 . 49 .50

Answer 1

Đặt A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 48.49.50

4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ... + 48.49.50.4

4A = 1.2.3.4 + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) + ... + 48.49.50.(51 - 47)

4A = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + 48.49.50.51 - 47.48.49.50

4A = 48.49.50.51

A = 48.49.50.51 : 4

A = 1499400

Answer 2

1.2.3 + 2.3.4 + 3.4.5 + ... + 48.49.50

Đặt A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 48.49.50

    4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ... + 48.49.50.4

    4A = 1.2.3.4 + 2.3.4.(5-1) + 3.4.5.(6-2) + ... + 48.49.50.(51-47)

    4A = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + 48.49.50.51 - 47.48.49.50

    4A = ( 1.2.3.4 + 2.3.4.5 + 3.4.5.6 + ... + 48.49.50.51 ) - ( 1.2.3.4 - 2.3.4.5 - 47.48.49.50 )

    4A = \(\frac{48.49.50.51}{4}\)

      A = 1499400