Definition:Triangular Number/Definition 2

Definition

Triangular numbers are defined as:

$\displaystyle T_n = \sum_{i \mathop = 1}^n i = 1 + 2 + \cdots + \left({n-1}\right) + n$

for $n = 1, 2, 3, \ldots$

Examples of Triangular Numbers

The first few triangular numbers are as follows:

Sequence of Triangular Numbers

The sequence of triangular numbers, for $n \in \Z_{\ge 0}$, begins:

$0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, \ldots$