Question

Tính A = 1.2 + 2.3 + 3.4 + … + n.(n + 1)

Answer 1

ta có : A = 1.2 + 2.3 + 3.4 + … + n.(n + 1)

 => 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + n.(n + 1).(n + 2)

=> 3A = n.(n + 1).(n + 2)

=> A = n.(n + 1).(n + 2)/3

Answer 2

nhân 3 hai vế ta được

3A=3.[1.2+ 2.3+ 3.4 + ....+(n-1).n]

3A=1.2.3 + 2.3.3 +3.4.3 + ...(n-1).n.3

3A=1.2.3 + 2.3.(4-1) +3.4.(5-2) + (n-1).n.[(n+1) -(n-2)]

3A=(n-1).n.(n+1)

A=(n-1).n.(n+1) : 3

.thank you !!!!!!!!!!!!!!!!!!