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

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:

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

Also see

• Equivalence of Definitions of Triangular Number

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {1-1}$ Principle of Mathematical Induction