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http://en.wikipedia.org/wiki/Triangular_number

I am looking at Triangle numbers and how wikipedia arrived at test for "Triangularity" by checking $(\sqrt{8x + 1} - 1)/2$

The article references item 4 but that does not seem to provide any proof.

can someone help me with references?

1 Answers 1

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It comes from solving the equation $\frac{n(n+1)}{2}=x$ for $n$, where $x$ and $n$ are non-negative. The solutions obtained are $n=\frac{-1\pm \sqrt{1+8x}}{2},$ and we throw away the negative solution.

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    Aaha you are right if we apply the "standard" quadratic formula http://en.wikipedia.org/wiki/Quadratic_equation this solves it for me! Cool thanks2012-10-17