Some application of elements of the theory of finite boundaries to solving problems in mathematical analysis

Abstract

In this article the expediency of using the apparatus of finite difference theory to calculate sums. Examples of finding sums based on the application of the properties of a difference and a discriminant operator are given. The differences and common features between the properties of solutions of the simplest difference and differential equations are indicated. The advantages and disadvantages of finding a common member of the sequence of Fibonacci numbers with the help of a recurrence relation and how to solve a corresponding difference equation are found out.