Prove by mathematical induction that $\displaystyle\sum_{r=1}^{n}r(r+2)=\dfrac{n(n+1)(2n+7)}{6}$ f

Question

Prove by mathematical induction that $\displaystyle\sum_{r=1}^{n}r(r+2)=\dfrac{n(n+1)(2n+7)}{6}$ for every $n\in\mathbb Z^+$.

Accepted Answer

$\displaystyle\sum_{r=1}^{n}r(r+2)=\dfrac{n(n+1)(2n+7)}{6}$ for every $n\in\mathbb Z^+$.

Sum of Shifted Products