Question

[Hà_Bảo_Trâm]

tính tổng :

A=4 x 5 + 5 x 6 + 6 x 7 +...... 30 x 31

Answer 1

[Phan Thanh Tịnh]

A = 4.5 + 5.6 + 6.7 + ... + 30.31

3A = 3.4.5 + 3.5.6 + 3.6.7 + ... + 3.30.31

     = (6 - 3).4.5 + (7 - 4).5.6 + (8 - 5).6.7 + ... + (32 - 29).30.31

     = 4.5.6 - 3.4.5 + 5.6.7 - 4.5.6 + 6.7.8 - 5.6.7 + ... + 30.31.32 - 29.30.31

     = (4.5.6 + 5.6.7 + 6.7.8 + ... + 30.31.32) - (3.4.5 + 4.5.6 + 5.6.7 + ... + 29.30.31)

     = 30.31.32 - 3.4.5 = 29760 - 60 = 29700

A = 29700 : 3 = 9900