## New Expression of the Factorial of $n$ ($n!$, $n\in N$)

**Authors:** S Maiti

New Expression of the factorial of $n$ ($n!$, $n\in N$) is given in
this article. The general expression of it has been proved with help
of the Principle of Mathematical Induction. It is found in the form
\begin{equation}
1+\sum_{i=1}^{n}a_i
+\sum_{\substack{i,j=1 \\(i<j)}}^{n}a_ia_j +
\sum_{\substack{i,j,k=1 \\(i<j<k)}}^{n}a_ia_ja_k +\cdots
+a_1a_2\cdots a_{n},
\label{factorial_expression}
\end{equation}
where $a_i=i-1$ for $i=1,~2,~\cdots ,~n$. More convenient expression
of this form is provided in Appendix.

**Comments:** 4 Pages.

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### Submission history

[v1] 2012-07-23 15:12:20

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