Question

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

Answer 1

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

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

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

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

=> A = \(\frac{\text{n.(n+1).(n+2)}}{3}\)