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Odd Number Theorem

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OddNumberTheorem

The sum of the first n odd numbers is a square number,

sum_(k=1)^n(2k-1)=n^2.

A sort of converse also exists, namely the difference of the nth and (n-1)st square numbers is the nth odd number, which follows from

n^2-(n-1)^2=2n-1.

See also

Gnomonic Number, Nicomachus's Theorem, Odd Number, Sum

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Cite this as:

Weisstein, Eric W. "Odd Number Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OddNumberTheorem.html

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