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Benedict Irwin edited Random.tex
over 9 years ago
Commit id: 0b5328e1132cf467a555e018332e8f12ea1bc098
deletions | additions
diff --git a/Random.tex b/Random.tex
index 7d76c8e..0187e25 100644
--- a/Random.tex
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...
\end{equation}
Is there something special about $12$
then, such that \begin{equation}
\prod_{n=0}^{\infty}\frac{e^{12n}}{n!} = 1
\end{equation}
But then, it must be true, as $log(1)=0$ that \begin{equation}
\sum_{n=1}^\infty 12n - log(n!) =0
\end{equation}
Which can be rewritten as \begin{equation}
12\sum_{n=1}^\infty n = \sum_{n=1}^\infty log(n!)
\end{equation}
However we know the sum on the left hand side to be $-1/12$ such that \begin{equation}
\sum_{n=1}^\infty log(n!) = -1
\end{equation} then...