Definition:Triangular Number

Definition
Triangular numbers are those denumerating a collection of objects which can be arranged in the form of an equilateral triangle.

They are often denoted $T_1, T_2, T_3, \ldots$, and they are formally defined as:
 * $\displaystyle T_n = \sum_{i \mathop = 1}^n i = 1 + 2 + \cdots + \left({n-1}\right) + n$

Also known as
Triangular numbers are also known as triangle numbers.

Also see
0 & : n = 0 \\ n + T_{n-1} & : n > 0 \end{cases}$
 * Recurrence Relation for Triangular Numbers: $T_n = \begin{cases}


 * Closed Form for Triangular Numbers: $T_n = \dfrac {n \left({n + 1}\right)} 2$