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[parent] sum of odd numbers (Example)
StrictlyEvenCode

"sum of odd numbers" is owned by pahio.
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See Also: odd number


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Cross-references: consecutive, row, triangle, odd numbers, number, arithmetic mean, arithmetic progression, odd integers, positive, sum
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This is version 12 of sum of odd numbers, born on 2004-09-25, modified 2007-12-20.
Object id is 6230, canonical name is SumOfOddNumbers.
Accessed 18068 times total.

Classification:
AMS MSC00A05 (General :: General and miscellaneous specific topics :: General mathematics)
 11B25 (Number theory :: Sequences and sets :: Arithmetic progressions)

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Geometric proof by rm50 on 2007-12-20 08:03:35
There's also the standard geometric 'proof' of this statement that you might want to add. Draw a square matrix of dots. Then the size of the set of dots
\{S_n=(x,y) | x\leq n, y=n or y\leq n, x=n\}
is 2n+1; regarding each of these as a shell, as you add shells, you clearly get the next square.

Roger
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sum of even numbers by perucho on 2004-10-12 01:11:58

And adding 1 to each number, in Mr. pahio entry (Hi my friend!), we get the sum of n first even numbers, i.e. n^2+n=n(n+1).
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