**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**

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

**Unique-IP document downloads:** 242 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful. *