1) For an integer n≥1,∑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(n−1)(2n+8)6 Answer: Option BExplanation:Consider, ∑nk=1k(k+2)=∑nk=1(k2+2k)=∑nk=1k2+2∑nk=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