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:
Sequence of Square Numbers
The sequence of square numbers, for $n \in \Z_{\ge 0}$, begins:
- $0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, \ldots$