Bi-Directional Infinity Box

Abstract

The following article introduces a new concept of Bi-directional Box. The concept is explained by simultaneously calculating a new result: sum of all the natural multiples of each natural number upto infinity. The concept of Bi-directional Box helps to organise multiple infinite series and study different patterns in multiple infinite series. This Bi-directional box can be converted into a triangle by rearranging the already organised terms of the initial box. Similar to Pascal's triangle, this box has many patterns and properties instilled in it too. Along with the initial standard box, infinite such boxes can be made depending upon the sequence/series in which the pattern is to be observed: an example with different sequences is provided at the end of the article.