Definition:Square Number/Definition 3

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Definition

Square numbers are defined as:

$\ds S_n = \sum_{i \mathop = 1}^n \paren {2 i - 1} = 1 + 3 + 5 + \cdots + \paren {2 n - 1}$

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


Examples of Square Numbers

The first few square numbers are as follows:

SquareNumbers.png


Sequence of Square Numbers

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

$0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, \ldots$


Also see