On a new general method of summation

TL;DR

The paper introduces a novel, unified summation method based on integer reordering that provides explicit formulas and assigns limits to oscillating functions, advancing summation theory.

Contribution

It presents a new general summation technique that is regular, consistent, and includes explicit formulas, expanding the tools for summation and limit assignment.

Findings

Includes explicit closed-form summation formulas.

Provides a method to assign limits to unbounded or oscillating functions.

Proposes a unified approach based on integer reordering.

Abstract

A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation formulas, and assigns limits to certain unbounded or oscillating functions. Some problems and future lines of research are briefly discussed.