Tính A = 1.2 + 2.3 + 3.4 + + n(n + 1)
Tính A = 1.2 + 2.3 + 3.4 + ... + n(n + 1).
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 \(A = \frac{{n\left( {n + 1} \right)\left( {n + 2} \right)}}{3}\).