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

Question

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

Accepted Answer

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

Sum of Triangular Numbers