Tính A = 1.2 + 2.3 + 3.4 + + n(n + 1)

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

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

3A= 1.2.(3 −0) + 2.3.(4 − 1) + 3.4.(5 −2)+ … +n(n + 1)[(n + 2) −(n + 1)]

3A=1.2.3 + 2.3.4 − 1.2.3 + 3.4.5 −2.3.4+ … +n(n + 1)(n + 2) −(n −1)n(n + 1)

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

Vậy \(A = \frac{{n\left( {n + 1} \right)\left( {n + 2} \right)}}{3}\).