Definition:Triangular Number/Definition 1

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Definition

Triangular numbers are defined as

$T_n = \begin{cases} 0 & : n = 0 \\ n + T_{n-1} & : n > 0 \end{cases}$

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


Examples of Triangular Numbers

The first few triangular numbers are as follows:

TriangleNumbers.png


Sequence of Triangular Numbers

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

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


Also see


Sources