Question

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

Answer 1

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

   =( 1.2.3- 0.1.2) +(2.3.4-1.2.3) +( 3.4.5 - 2.3.4)+...............+( n(n+1)(n+2) - (n-1)n(n+1))

  = 1.2.3 -0.1.2 + 2.3.4-1.2.3 + 3.4.5 - 2.3.4  + ...............+ n(n+1)(n+2)  -  (n-1)n(n+1)

  = n(n+1)(n+2)

=> A    = n(n+1)(n+2)/3