Closed Form for Triangular Numbers/Proof by Polygonal Numbers

Proof
Triangular numbers are $k$-gonal numbers where $k = 3$.

Hence from Closed Form for Polygonal Numbers we have that:
 * $T_n = \dfrac {n \left({2 + \left({n - 1}\right) \left({k - 2}\right)}\right)} 2$

where $k = 3$.

The result follows after some simple algebra.