For any integer n ≥1, then ∑k=1nk(k+2) is equal to - Maths - Principle of Mathematical Induction

Question

For any integer n ≥ 1, then ∑ k = 1 n k ( k + 2 )
  is equal to?

Lovina Kansal · Accepted Answer

Dear student
∑k=1nk(k+2)=∑k=1nk2+2k=∑k=1nk2+2∑k=1nk=n(n+1)(2n+1)6+2n(+1)2=n(n+1)(2n+1)6+n(n+1)=n(n+1)(2n+1)+6n(n+1)6=n(n+1)2n+1+66=n(n+1)(2n+7)7
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For any integer n ≥ 1, then ∑ k = 1 n k ( k + 2 ) is equal to?

For any integer n $\geq$ 1, then $\sum_{k = 1}^{n} k (k + 2)$ is equal to?