IDENTIFYING SEQUENCE $\left\{a_n\right\}$ USING THE SUMS $S_n$

Abstract

A popular way to identify the sequence $\left\{a_n\right\}$ using the sums $S_n$ is to use $S_n-S_{n-1}$. In this paper, we propose an alternative method. In reference [1], we introduced that the sum $S_n$ can be calculated using dimensions. According to this, the dimension of $S_n$ is one higher than the dimension of $a_n$. For example, if $S_n$ is a quadratic expression of $n$, then $a_n$ is a linear expression of $n$. Thus, $a_n$ can be identified by finding the coefficients of this linear expression.

Received: January 17, 2024
Accepted: March 4, 2024