1)

For an integer  n1,nk=1K(K+2)=


A) n(n+1)(n+2)6

B) n(n+1)(2n+7)6

C) n(n+1)(2n+1)6

D) n(n1)(2n+8)6

Answer:

Option B

Explanation:

Consider,

nk=1k(k+2)=nk=1(k2+2k)=nk=1k2+2nk=1k

    =n(n+1)(2n+1)6+2n(n+1)2

      =n(n+1)[(2n+1)6+1]=n(n+1)[2n+76]

  =n(n+1)(2n+7)6