## Important Relations Over Some Summations $\left(\displaystyle \sum_{\substack{i,j=1\\(i<j)}}^{n}ij,~\sum_{\substack{i,j,k=1\\(i<j<k)}}^{n}ijk,~\sum_{\substack{i,j,k,l=1 \\(i<j<k<l)}}^{n}ijkl,~\cdots \right)$

**Authors:** S. Maiti

The paper is focused to find important relations and identities over
some summations for natural numbers such as $\displaystyle
\sum_{\substack{i,j=1\\(i<j)}}^{n}ij,~\sum_{\substack{i,j,k=1\\(i<j<k)}}^{n}ijk,~\sum_{\substack{i,j,k,l=1
\\(i<j<k<l)}}^{n}ijkl,~\cdots $. These relations are believed to
find applications in the various branches of number theory
particularly in the proposed theorems of Maiti
\cite{Maiti1,Maiti2,Maiti3,Maiti4,Maiti5} which help to represent the
factorial $n!$ entirely new way and also help to exhibit the $n$th
partial sum of the general harmonic series $\displaystyle
\sum_{n=1}^{\infty} \frac{1}{a+(n-1) b}$ and its particular
cases.

**Comments:** 5 Pages.

**Download:** **PDF**

### Submission history

[v1] 2012-07-24 13:15:05

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