Prove by mathematical induction that \(\displaystyle\sum_{r=1}^{n} r(r+1)=\dfrac{n(n+1)(n+2)}3\

Question

Prove by mathematical induction that $\displaystyle\sum_{r=1}^{n} r(r+1)=\dfrac{n(n+1)(n+2)}3$ for every $n\in\mathbb Z^+$.

Accepted Answer

$\displaystyle\sum_{r=1}^{n} r(r+1)=\dfrac{n(n+1)(n+2)}3$

A Summation Identity