Definition:Triangular Number/Definition 1

Definition
Triangular numbers are defined as
 * $T_n = \begin{cases}

0 & : n = 0 \\ n + T_{n-1} & : n > 0 \end{cases}$ for $n = 1, 2, 3, \ldots$

Also see

 * Equivalence of Definitions of Triangular Number