SIMPLE SUM CALCULATION USING DIMENSIONS

Abstract

Let us consider the sum of $n$ integers. If each integer value is the length of a bar, the sum is the collection of bars, which is the two-dimensional area. In other words, the sum of $n$ integers should be a quadratic expression of $n$. It is easy to identify the coefficients of this quadratic expression. Similarly, let us consider the sum of $n$ square numbers. If each square number value is taken as area, the sum is the collection of areas, which is the three-dimensional volume. In other words, the sum of $n$ square numbers should be a cubic expression of $n.$  It is easy to identify the coefficients of this cubic expression. As shown above, various sums can be easily calculated using dimensions.

Received: November 10, 2023
Accepted: November 29, 2023